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

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


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

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

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

Reorder the terms for easier multiplication:
4 * 4(-1 + 3x)(-1 + 3x) = 100

Multiply 4 * 4
16(-1 + 3x)(-1 + 3x) = 100

Multiply (-1 + 3x) * (-1 + 3x)
16(-1(-1 + 3x) + 3x * (-1 + 3x)) = 100
16((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 100
16((1 + -3x) + 3x * (-1 + 3x)) = 100
16(1 + -3x + (-1 * 3x + 3x * 3x)) = 100
16(1 + -3x + (-3x + 9x2)) = 100

Combine like terms: -3x + -3x = -6x
16(1 + -6x + 9x2) = 100
(1 * 16 + -6x * 16 + 9x2 * 16) = 100
(16 + -96x + 144x2) = 100

Solving
16 + -96x + 144x2 = 100

Solving for variable 'x'.

Reorder the terms:
16 + -100 + -96x + 144x2 = 100 + -100

Combine like terms: 16 + -100 = -84
-84 + -96x + 144x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-84 + -96x + 144x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-7 + -8x + 12x2) = 0

Factor a trinomial.
12((-1 + -2x)(7 + -6x)) = 0

Ignore the factor 12.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-0.5, 1.166666667}

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