(x-1)(x-1)3=144

Solution for (x-1)(x-1)3=144 equation:

Simplifying
(x + -1)(x + -1) * 3 = 144

Reorder the terms:
(-1 + x)(x + -1) * 3 = 144

Reorder the terms:
(-1 + x)(-1 + x) * 3 = 144

Reorder the terms for easier multiplication:
3(-1 + x)(-1 + x) = 144

Multiply (-1 + x) * (-1 + x)
3(-1(-1 + x) + x(-1 + x)) = 144
3((-1 * -1 + x * -1) + x(-1 + x)) = 144
3((1 + -1x) + x(-1 + x)) = 144
3(1 + -1x + (-1 * x + x * x)) = 144
3(1 + -1x + (-1x + x2)) = 144

Combine like terms: -1x + -1x = -2x
3(1 + -2x + x2) = 144
(1 * 3 + -2x * 3 + x2 * 3) = 144
(3 + -6x + 3x2) = 144

Solving
3 + -6x + 3x2 = 144

Solving for variable 'x'.

Reorder the terms:
3 + -144 + -6x + 3x2 = 144 + -144

Combine like terms: 3 + -144 = -141
-141 + -6x + 3x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-141 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-47 + -2x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-47 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-47 + -2x + x2 = 0

Solving
-47 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -2x + 47 + x2 = 0 + 47

Reorder the terms:
-47 + 47 + -2x + x2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -2x + x2 = 0 + 47
-2x + x2 = 0 + 47

Combine like terms: 0 + 47 = 47
-2x + x2 = 47

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 47 + 1

Reorder the terms:
1 + -2x + x2 = 47 + 1

Combine like terms: 47 + 1 = 48
1 + -2x + x2 = 48

Factor a perfect square on the left side:
(x + -1)(x + -1) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + -1) equal to 6.92820323 and -6.92820323.

Subproblem 1
x + -1 = 6.92820323

Simplifying
x + -1 = 6.92820323

Reorder the terms:
-1 + x = 6.92820323

Solving
-1 + x = 6.92820323

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.92820323 + 1
x = 6.92820323 + 1

Combine like terms: 6.92820323 + 1 = 7.92820323
x = 7.92820323

Simplifying
x = 7.92820323

Subproblem 2
x + -1 = -6.92820323

Simplifying
x + -1 = -6.92820323

Reorder the terms:
-1 + x = -6.92820323

Solving
-1 + x = -6.92820323

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.92820323 + 1
x = -6.92820323 + 1

Combine like terms: -6.92820323 + 1 = -5.92820323
x = -5.92820323

Simplifying
x = -5.92820323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.92820323, -5.92820323}
Solution
x = {7.92820323, -5.92820323}