3(x-6)(x-6)=75

Solution for 3(x-6)(x-6)=75 equation:

Simplifying
3(x + -6)(x + -6) = 75

Reorder the terms:
3(-6 + x)(x + -6) = 75

Reorder the terms:
3(-6 + x)(-6 + x) = 75

Multiply (-6 + x) * (-6 + x)
3(-6(-6 + x) + x(-6 + x)) = 75
3((-6 * -6 + x * -6) + x(-6 + x)) = 75
3((36 + -6x) + x(-6 + x)) = 75
3(36 + -6x + (-6 * x + x * x)) = 75
3(36 + -6x + (-6x + x2)) = 75

Combine like terms: -6x + -6x = -12x
3(36 + -12x + x2) = 75
(36 * 3 + -12x * 3 + x2 * 3) = 75
(108 + -36x + 3x2) = 75

Solving
108 + -36x + 3x2 = 75

Solving for variable 'x'.

Reorder the terms:
108 + -75 + -36x + 3x2 = 75 + -75

Combine like terms: 108 + -75 = 33
33 + -36x + 3x2 = 75 + -75

Combine like terms: 75 + -75 = 0
33 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -12x + x2) = 0

Factor a trinomial.
3((1 + -1x)(11 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {1, 11}