6(x-6)(x-6)=42

Solution for 6(x-6)(x-6)=42 equation:

Simplifying
6(x + -6)(x + -6) = 42

Reorder the terms:
6(-6 + x)(x + -6) = 42

Reorder the terms:
6(-6 + x)(-6 + x) = 42

Multiply (-6 + x) * (-6 + x)
6(-6(-6 + x) + x(-6 + x)) = 42
6((-6 * -6 + x * -6) + x(-6 + x)) = 42
6((36 + -6x) + x(-6 + x)) = 42
6(36 + -6x + (-6 * x + x * x)) = 42
6(36 + -6x + (-6x + x2)) = 42

Combine like terms: -6x + -6x = -12x
6(36 + -12x + x2) = 42
(36 * 6 + -12x * 6 + x2 * 6) = 42
(216 + -72x + 6x2) = 42

Solving
216 + -72x + 6x2 = 42

Solving for variable 'x'.

Reorder the terms:
216 + -42 + -72x + 6x2 = 42 + -42

Combine like terms: 216 + -42 = 174
174 + -72x + 6x2 = 42 + -42

Combine like terms: 42 + -42 = 0
174 + -72x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(29 + -12x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(29 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
29 + -12x + x2 = 0

Solving
29 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -12x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + -12x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -12x + x2 = 0 + -29
-12x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
-12x + x2 = -29

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -29 + 36

Reorder the terms:
36 + -12x + x2 = -29 + 36

Combine like terms: -29 + 36 = 7
36 + -12x + x2 = 7

Factor a perfect square on the left side:
(x + -6)(x + -6) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -6) equal to 2.645751311 and -2.645751311.

Subproblem 1
x + -6 = 2.645751311

Simplifying
x + -6 = 2.645751311

Reorder the terms:
-6 + x = 2.645751311

Solving
-6 + x = 2.645751311

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 2.645751311 + 6

Combine like terms: -6 + 6 = 0
0 + x = 2.645751311 + 6
x = 2.645751311 + 6

Combine like terms: 2.645751311 + 6 = 8.645751311
x = 8.645751311

Simplifying
x = 8.645751311

Subproblem 2
x + -6 = -2.645751311

Simplifying
x + -6 = -2.645751311

Reorder the terms:
-6 + x = -2.645751311

Solving
-6 + x = -2.645751311

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -2.645751311 + 6

Combine like terms: -6 + 6 = 0
0 + x = -2.645751311 + 6
x = -2.645751311 + 6

Combine like terms: -2.645751311 + 6 = 3.354248689
x = 3.354248689

Simplifying
x = 3.354248689

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.645751311, 3.354248689}
Solution
x = {8.645751311, 3.354248689}