4x(x-2)-5x(x-1) = 2?

4x(x-2)-5x(x-1) = 2 multiply it out

4x² - 8x - 5x²+ 5x = 2 subtract 2 and combine like terms:

-x² -3x - 2 = 0 Multiply through by -1

x² + 3x + 2 = 0 Factor:

(x )(x ) Place 'x's. Ask yourself, which two numbers when added together equal 3, but when multiplied equal 2. (1,2)

(x + 1)(x + 2 ) Now ask yourself what values of x will make the equation equal to zero? ( -1, -2)

x = -1 and -2

4x(x - 2) - 5x(x - 1) = 2
4x² - 8x - 5x² + 5x = 2
- x² - 3x = 2
x² + 3x + 2 = 0
(x + 1)(x + 2) = 0
x + 1 = 0 . . . or . . . x + 2 = 0
x = - 1 . . . or . . . x = - 2

Alejandra

First, multiply out the brackets to get:

4x^2 - 8x - 5x^2 + 5x = 2

Note, it is + 5x because minus * minus = +

Now collect like terms and simplify to get:

-x^2 - 3x = 2

x^2 + 3x + 2 = 0

You probably recognise this as a quadratic equation which can be solved by several methods. Factorising is the simplest. We get:

x^2 + 2x + x + 2 = 0

x(x + 2) + 1(x+ 2) = 0

(x + 2)(x +1) = 0

So (x + 2) = 2 or (x + 1) = 0

x = -2 or x = -1 which are the solutions for x.

It is a good idea to check these out by substituting for x in the original equation. For example:

4(-2)(-2 -2) - 5*(-2)(-2 - 1)

= (-8)*(-4) + 10* (-3)

= 32 - 30

= 2 as expected

4x(x-2)-5x(x-1)=2
4x^2-8x-5x^2+5x=2
-x^2-3x=2
0=x^2+3x+2
0=(x+2)(x+1)
x={-1,-2}

4x^2 - 8x - 5x^2 + 5x = 2

- x^2 - 3x = 2

- x^2 - 3x - 2 = 0

x^2 + 3x + 2 = 0

(x+ 2)(x+1) =0

x+ 2 = 0, so x = -2

x+1 = 0, so x = -1

4x² - 8x - 5x² + 5x = 2
- x² - 3x - 2 = 0
x² + 3x + 2 = 0
(x + 1)(x + 2) = 0
x = - 1 , x = - 2

4x(x-2)-5x(x-1) = 2
multiplying out the brackets gives:
4x^2 - 8x - 5x^2 + 5x = 2
Now collect the like terms:
-x^2 - 3x = 2
move 2 to the other side and multiply the expression by -1:
-x^2 - 3x - 2 = 0
x^2 + 3x + 2 = 0
factorise to give:
(x + 2) (x + 1)= 0
therefore x = -2 or x = -1
Hope this helps!

4x(x - 2) - 5x(x - 1) = 2
4x*x - 4x*2 - 5x*x + 5x*1 = 2
4x^2 - 8x - 5x^2 + 5x = 2
4x^2 - 5x^2 - 8x + 5x - 2 = 0
-x^2 - 3x - 2 = 0
-x^2 - x - 2x - 2 = 0
-x(x + 1) - 2(x + 1) = 0
(x + 1)(-x - 2) = 0

x + 1 = 0
x = -1

-x - 2 = 0
-x = 2
x = 2/-1
x = -2

∴ x = -1 , -2

I'm not going to do your homework for you, but I'll do a similar one so you can see how to do this one.
In general, just remember that:
a(b + c) = ab + ac

So, let's do:
7y(y + 3) - 2y(y - 8) = 156
7yy + 7y3 - 2yy + 2y8 = 156
Notice that for "+2y8" the two minus signs canceled each other out. Another way to write the previous step would have been 7yy + 7y3 + (-2)yy + (-2)y(-8). And obvious -2 times -8 is 16. And yy = "y squared" but that's hard to type so I'll stick with yy. So, the next step is:
7yy + 21y - 2yy + 16y = 156
Re-arrange, and get:
7yy - 2yy + 21y + 16y = 156
It doesn't matter what "y" is, 21 of something plus 16 of the same thing equals 37 of that thing. So:
7yy - 2yy + 37y = 156
Likewise, it doesn't matter what "yy" is, but 7 of anything minus 2 of that thing equals 5 of that thing. So:
5yy + 37y = 156
We often like to move everything over to the left, so let's subtract 156 from both sides:
5yy + 37y - 156 = 156 - 156
5yy + 37y - 156 = 0

So far all we've done is move stuff around, to get it into the format Ayy + By + C = 0 (or with any of the plusses as minusses instead). In the case of the equation above, A is 5, B is 37 and C is -156. Now we bring out the big ugly:

(-B + or - squareroot(BB - 4AC)) / 2A
That's called the quadratic equation and works as long as you have "something squared" as the highest power in the equation. It won't work if you have anything cubed, to the 4th power, etc. But you don't in this problem. So:
(-37 plus or minus squareroot (37*37 - 4*5*(-156))) / (2*5)
(-37 plus or minus squareroot (1369 - (-3120))) / 10
(-37 plus or minus squareroot(1369 + 3120)) / 10
(-37 plus or minus squareroot(4489)) / 10
(-37 plus or minus 67) / 10
(-37 - 67) / 10 or (-37 + 67) / 10
-104 / 10 or 30 /10
-10.4 or 3
And there you go. -10.4 and 3 are both correct value for y.

4x(x-2)-5x(x-1)=2
4x^2-8-5x^2+5x=2
-x^2+5x-8=2
5x-x^2=10
x(5-x)=10
x=10/(5-x)

I think. It's been while since I did algebra.