2(3x-1)(3x-1)-8=0

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Solution for 2(3x-1)(3x-1)-8=0 equation: 


Simplifying
2(3x + -1)(3x + -1) + -8 = 0

Reorder the terms:
2(-1 + 3x)(3x + -1) + -8 = 0

Reorder the terms:
2(-1 + 3x)(-1 + 3x) + -8 = 0

Multiply (-1 + 3x) * (-1 + 3x)
2(-1(-1 + 3x) + 3x * (-1 + 3x)) + -8 = 0
2((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) + -8 = 0
2((1 + -3x) + 3x * (-1 + 3x)) + -8 = 0
2(1 + -3x + (-1 * 3x + 3x * 3x)) + -8 = 0
2(1 + -3x + (-3x + 9x2)) + -8 = 0

Combine like terms: -3x + -3x = -6x
2(1 + -6x + 9x2) + -8 = 0
(1 * 2 + -6x * 2 + 9x2 * 2) + -8 = 0
(2 + -12x + 18x2) + -8 = 0

Reorder the terms:
2 + -8 + -12x + 18x2 = 0

Combine like terms: 2 + -8 = -6
-6 + -12x + 18x2 = 0

Solving
-6 + -12x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -2x + 3x2) = 0

Factor a trinomial.
6((-1 + -3x)(1 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.3333333333, 1}

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