(3x-2)(3x-2)=16

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Solution for (3x-2)(3x-2)=16 equation: 


Simplifying
(3x + -2)(3x + -2) = 16

Reorder the terms:
(-2 + 3x)(3x + -2) = 16

Reorder the terms:
(-2 + 3x)(-2 + 3x) = 16

Multiply (-2 + 3x) * (-2 + 3x)
(-2(-2 + 3x) + 3x * (-2 + 3x)) = 16
((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 16
((4 + -6x) + 3x * (-2 + 3x)) = 16
(4 + -6x + (-2 * 3x + 3x * 3x)) = 16
(4 + -6x + (-6x + 9x2)) = 16

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) = 16

Solving
4 + -12x + 9x2 = 16

Solving for variable 'x'.

Reorder the terms:
4 + -16 + -12x + 9x2 = 16 + -16

Combine like terms: 4 + -16 = -12
-12 + -12x + 9x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-12 + -12x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -4x + 3x2) = 0

Factor a trinomial.
3((-2 + -3x)(2 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
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
Solution
x = {-0.6666666667, 2}

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