(3x-2)(3x-2)=100

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Solution for (3x-2)(3x-2)=100 equation: 


Simplifying
(3x + -2)(3x + -2) = 100

Reorder the terms:
(-2 + 3x)(3x + -2) = 100

Reorder the terms:
(-2 + 3x)(-2 + 3x) = 100

Multiply (-2 + 3x) * (-2 + 3x)
(-2(-2 + 3x) + 3x * (-2 + 3x)) = 100
((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 100
((4 + -6x) + 3x * (-2 + 3x)) = 100
(4 + -6x + (-2 * 3x + 3x * 3x)) = 100
(4 + -6x + (-6x + 9x2)) = 100

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) = 100

Solving
4 + -12x + 9x2 = 100

Solving for variable 'x'.

Reorder the terms:
4 + -100 + -12x + 9x2 = 100 + -100

Combine like terms: 4 + -100 = -96
-96 + -12x + 9x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-96 + -12x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-32 + -4x + 3x2) = 0

Factor a trinomial.
3((-8 + -3x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2.666666667, 4}

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