4(3x-1)(3x-1)=100

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Solution for 4(3x-1)(3x-1)=100 equation: 


Simplifying
4(3x + -1)(3x + -1) = 100

Reorder the terms:
4(-1 + 3x)(3x + -1) = 100

Reorder the terms:
4(-1 + 3x)(-1 + 3x) = 100

Multiply (-1 + 3x) * (-1 + 3x)
4(-1(-1 + 3x) + 3x * (-1 + 3x)) = 100
4((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 100
4((1 + -3x) + 3x * (-1 + 3x)) = 100
4(1 + -3x + (-1 * 3x + 3x * 3x)) = 100
4(1 + -3x + (-3x + 9x2)) = 100

Combine like terms: -3x + -3x = -6x
4(1 + -6x + 9x2) = 100
(1 * 4 + -6x * 4 + 9x2 * 4) = 100
(4 + -24x + 36x2) = 100

Solving
4 + -24x + 36x2 = 100

Solving for variable 'x'.

Reorder the terms:
4 + -100 + -24x + 36x2 = 100 + -100

Combine like terms: 4 + -100 = -96
-96 + -24x + 36x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-96 + -24x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-8 + -2x + 3x2) = 0

Factor a trinomial.
12((-4 + -3x)(2 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
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

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 = {-1.333333333, 2}

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