2(3x-2)*2(3x-2)+7=23

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Solution for 2(3x-2)*2(3x-2)+7=23 equation: 


Simplifying
2(3x + -2) * 2(3x + -2) + 7 = 23

Reorder the terms:
2(-2 + 3x) * 2(3x + -2) + 7 = 23

Reorder the terms:
2(-2 + 3x) * 2(-2 + 3x) + 7 = 23

Reorder the terms for easier multiplication:
2 * 2(-2 + 3x)(-2 + 3x) + 7 = 23

Multiply 2 * 2
4(-2 + 3x)(-2 + 3x) + 7 = 23

Multiply (-2 + 3x) * (-2 + 3x)
4(-2(-2 + 3x) + 3x * (-2 + 3x)) + 7 = 23
4((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) + 7 = 23
4((4 + -6x) + 3x * (-2 + 3x)) + 7 = 23
4(4 + -6x + (-2 * 3x + 3x * 3x)) + 7 = 23
4(4 + -6x + (-6x + 9x2)) + 7 = 23

Combine like terms: -6x + -6x = -12x
4(4 + -12x + 9x2) + 7 = 23
(4 * 4 + -12x * 4 + 9x2 * 4) + 7 = 23
(16 + -48x + 36x2) + 7 = 23

Reorder the terms:
16 + 7 + -48x + 36x2 = 23

Combine like terms: 16 + 7 = 23
23 + -48x + 36x2 = 23

Add '-23' to each side of the equation.
23 + -48x + -23 + 36x2 = 23 + -23

Reorder the terms:
23 + -23 + -48x + 36x2 = 23 + -23

Combine like terms: 23 + -23 = 0
0 + -48x + 36x2 = 23 + -23
-48x + 36x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-48x + 36x2 = 0

Solving
-48x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(-4 + 3x) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-4 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Divide each side by '3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, 1.333333333}

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