-2(3x-2)(3x-2)=0

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Solution for -2(3x-2)(3x-2)=0 equation: 


Simplifying
-2(3x + -2)(3x + -2) = 0

Reorder the terms:
-2(-2 + 3x)(3x + -2) = 0

Reorder the terms:
-2(-2 + 3x)(-2 + 3x) = 0

Multiply (-2 + 3x) * (-2 + 3x)
-2(-2(-2 + 3x) + 3x * (-2 + 3x)) = 0
-2((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 0
-2((4 + -6x) + 3x * (-2 + 3x)) = 0
-2(4 + -6x + (-2 * 3x + 3x * 3x)) = 0
-2(4 + -6x + (-6x + 9x2)) = 0

Combine like terms: -6x + -6x = -12x
-2(4 + -12x + 9x2) = 0
(4 * -2 + -12x * -2 + 9x2 * -2) = 0
(-8 + 24x + -18x2) = 0

Solving
-8 + 24x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 12x + -9x2) = 0

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

Ignore the factor 2.

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 + -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
Solution
x = {0.6666666667, 0.6666666667}

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