(2x-3)(2x-3)=4x-6

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Solution for (2x-3)(2x-3)=4x-6 equation: 


Simplifying
(2x + -3)(2x + -3) = 4x + -6

Reorder the terms:
(-3 + 2x)(2x + -3) = 4x + -6

Reorder the terms:
(-3 + 2x)(-3 + 2x) = 4x + -6

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) = 4x + -6
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 4x + -6
((9 + -6x) + 2x * (-3 + 2x)) = 4x + -6
(9 + -6x + (-3 * 2x + 2x * 2x)) = 4x + -6
(9 + -6x + (-6x + 4x2)) = 4x + -6

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) = 4x + -6

Reorder the terms:
9 + -12x + 4x2 = -6 + 4x

Solving
9 + -12x + 4x2 = -6 + 4x

Solving for variable 'x'.

Reorder the terms:
9 + 6 + -12x + -4x + 4x2 = -6 + 4x + 6 + -4x

Combine like terms: 9 + 6 = 15
15 + -12x + -4x + 4x2 = -6 + 4x + 6 + -4x

Combine like terms: -12x + -4x = -16x
15 + -16x + 4x2 = -6 + 4x + 6 + -4x

Reorder the terms:
15 + -16x + 4x2 = -6 + 6 + 4x + -4x

Combine like terms: -6 + 6 = 0
15 + -16x + 4x2 = 0 + 4x + -4x
15 + -16x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
15 + -16x + 4x2 = 0

Factor a trinomial.
(3 + -2x)(5 + -2x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1.5, 2.5}

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