4(9x-1)=9 x(4-x) solve equation?

4(9x-1)=9x(4-x)
36x-4=36x-9x^2
-4=-9x^2
(4/9)=x^2
x=sqr(4/9)
x=+ and - (2/3)

a^2 - b^2 ≡ (a + b)(a - b)

4(9x - 1) = 9x(4 - x)
4(9x) - 4(1) = 9x(4) - 9x(x)
36x - 4 = 36x - 9x^2
9x^2 + 36x - 36x - 4 = 0
9x^2 - 4 = 0
(3x)^2 - 2^2 = 0
(3x + 2)(3x - 2) = 0

3x + 2 = 0
3x = -2
x = -2/3

3x - 2 = 0
3x = 2
x = 2/3

∴ x = ±2/3

4 (9x - 1) = 9x (4 - x)

First thing you have to do is distribute what's in the parenthesis.

4 * 9x + 4 * -1 = 9x * 4 + 9x * -x

36x - 4 = 36x - 9x²

Now, let's get x alone. But first, subtract 36x from both sides.

-4 = -9x²

Which is the same thing as:

4 = 9x²

by multiply or dividing each side by -1. I'm going to rearrange this so that x is on the left side rather than the right side, because I find it easier that way (personal preference, it doesn't really matter whether or not you do).

9x² = 4

Now, let's get x alone. 9 and x² are linked together by multiplication (9x² = 9 * x²), so let's do the inverse of multiplication to get x² alone.

Divide both sides by 9.

x² = 4/9

Now, since x is squared, we have to square root both sides. So,

(root)x² = (root)4/9

x = +or- 2/3

If you plug either of those two answers back into the original equation, they work. So we can assume that

x = 2/3 and - 2/3.

hope i helped :)

36x-4=36x-9x^2
9x^2-4=0
(3x-2)(3x+2)=0
x=2/3 & x=-2/3

4(9x-1) = 9 * x(4-x)
36x - 4 = 36x - 9x^2
9x^2 = 4
x^2 = 4/9
x = +- sqrt(4/9)
x = -2/3, 2/3

:D

78

4(9x-1)=9x(4-x)
.......36x-1=36x-x^2
.......x^2-1=0
.......X^2=1
.......x=1,-1

-9x*2 - 4

36X-4=36X-9X^2
THEREFORE 9X^2=4
X^2=4/9
X=2/3