12(x-1)(x-1)=75

Solution for 12(x-1)(x-1)=75 equation:

Simplifying
12(x + -1)(x + -1) = 75

Reorder the terms:
12(-1 + x)(x + -1) = 75

Reorder the terms:
12(-1 + x)(-1 + x) = 75

Multiply (-1 + x) * (-1 + x)
12(-1(-1 + x) + x(-1 + x)) = 75
12((-1 * -1 + x * -1) + x(-1 + x)) = 75
12((1 + -1x) + x(-1 + x)) = 75
12(1 + -1x + (-1 * x + x * x)) = 75
12(1 + -1x + (-1x + x2)) = 75

Combine like terms: -1x + -1x = -2x
12(1 + -2x + x2) = 75
(1 * 12 + -2x * 12 + x2 * 12) = 75
(12 + -24x + 12x2) = 75

Solving
12 + -24x + 12x2 = 75

Solving for variable 'x'.

Reorder the terms:
12 + -75 + -24x + 12x2 = 75 + -75

Combine like terms: 12 + -75 = -63
-63 + -24x + 12x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-63 + -24x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -8x + 4x2) = 0

Factor a trinomial.
3((-3 + -2x)(7 + -2x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1.5, 3.5}