6x(x-4)=0. I have the answer but don't understand why?

6x(x - 4) = 0

6x = 0
x = 0/6
x = 0

x - 4 = 0
x = 4

∴ x = 0, 4

You have to find the value of x

( 6x ) ( x - 4 ) = 0

6 x = 0 , x - 4 = 0

x = 0 , x = 4

The graph is a parabola that has 2 x-intercepts. So, after you distribute the 6x to make 6x^2 - 24x = 0, we can use completing the square to find the answer. Completing the square is a technique that lets you work on the left side of the equation only and have two answers.

So:
6x^2 - 24x + ___ = 0 - First we have to divide out the 6. (Make sure we remember to multiply by it again in the way I'll show)

6(x^2 - 4x + ____) = 0 - Next we divide 4, x's coefficient by 2 and square it.

6(x^2 - 4x + 4) = 0 - Third, we have to subtract 4x6 (because we took out that 6 at the beginning) from the left side to make it so we didn't add anything to the left side.

6(x^2 - 4x + 4) - 24 = 0 - Simplify by factoring

6(x-2)^2 - 24 = 0 - Now, we solve for x. Starting with adding 24 to both sides.

6(x-2)^2 = 24 - Divide by 6 on both sides.

(x-2)^2 = 4 - Square root both sides

x-2 = +2 and -2 - Then set x-2 = to each answer

x-2 = 2 ---> x=4

and

x-2 = -2 ----> x=0.

The answers are 0 and 4. Hope this helps!

To find the roots of the equation, you need to find all of the values of x that satisfy the equation. For 6x(x-4) = 0, solve the two different conditions that makes the right side = 0.

6x = 0, x = 0, and

x - 4 = 0, x = 4.

Because in that equation, you are getting the roots of the equation(x). So, using factoring equate it to zero and then it would be
6x=0 and x-4=0
find x
6x=0
x=0/6
x=0
find x again
x-4=0
add 4 to both sides to get the value of x
x-4+4=0+4
x=4
so the roots are (0,4)

Here you are finding x.

Because you are given the equation in factors already, it's easy. Just
know that if a group of factors are multiplied and they equal 0, it means that at least one equals 0.

So you equal them all to 0

6x(x-4)=0

6 =/= 0, so 6 isn't one of the x's
x = 0, so, 0 is the first x
x - 4 = 0
x = 4, so, 4 is the second and last x

And that's how you solve it.

The question has asked you to solve for x.

In this case,

6x = 0 and x - 4 = 0, giving you x = 0, x = 4.

" 6x(squared)-24x " is 6x(x - 4) expanded and hasn't been solved.

The question is what are the roots or zeros.

6x times (x-4) = 0

You 'defactored' (made up word) to 6x²-24x = 0, its the same equation but not an answer. So what will make this zero.
What makes 6x = 0? When x = 0
What makes (X-4) = 0? When x = 4
You can only do this if it is factored (simplified).

A really easy way to understand is just to plug in the values for x:

1) if x=0, then 6(0)(0-4)=0, so x=0 works

2) if x= 4, then 6(4)(4-4)=0, so x=4 works too.

the answer shouldn't be 6x (squared)-24x because they probably wanted you to find the value of 'x', and not just multiply the equation to make it simpler.

It depends on what they’re asking. 6X(X - 4) is the same as 6X^2 – 24X, but they set it equal to 0, meaning that they wanted you to solve for X. X= 0 and 4