x^2=4(2x-3)

Solution for x^2=4(2x-3) equation:

Simplifying
x2 = 4(2x + -3)

Reorder the terms:
x2 = 4(-3 + 2x)
x2 = (-3 * 4 + 2x * 4)
x2 = (-12 + 8x)

Solving
x2 = -12 + 8x

Solving for variable 'x'.

Reorder the terms:
12 + -8x + x2 = -12 + 8x + 12 + -8x

Reorder the terms:
12 + -8x + x2 = -12 + 12 + 8x + -8x

Combine like terms: -12 + 12 = 0
12 + -8x + x2 = 0 + 8x + -8x
12 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
12 + -8x + x2 = 0

Factor a trinomial.
(2 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {2, 6}