(X-6)(X-6)3=147

Solution for (X-6)(X-6)3=147 equation:

Simplifying
(X + -6)(X + -6) * 3 = 147

Reorder the terms:
(-6 + X)(X + -6) * 3 = 147

Reorder the terms:
(-6 + X)(-6 + X) * 3 = 147

Reorder the terms for easier multiplication:
3(-6 + X)(-6 + X) = 147

Multiply (-6 + X) * (-6 + X)
3(-6(-6 + X) + X(-6 + X)) = 147
3((-6 * -6 + X * -6) + X(-6 + X)) = 147
3((36 + -6X) + X(-6 + X)) = 147
3(36 + -6X + (-6 * X + X * X)) = 147
3(36 + -6X + (-6X + X2)) = 147

Combine like terms: -6X + -6X = -12X
3(36 + -12X + X2) = 147
(36 * 3 + -12X * 3 + X2 * 3) = 147
(108 + -36X + 3X2) = 147

Solving
108 + -36X + 3X2 = 147

Solving for variable 'X'.

Reorder the terms:
108 + -147 + -36X + 3X2 = 147 + -147

Combine like terms: 108 + -147 = -39
-39 + -36X + 3X2 = 147 + -147

Combine like terms: 147 + -147 = 0
-39 + -36X + 3X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + -12X + X2) = 0

Factor a trinomial.
3((-1 + -1X)(13 + -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 '(13 + -1X)' equal to zero and attempt to solve:

Simplifying
13 + -1X = 0

Solving
13 + -1X = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1X = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1X = 0 + -13
-1X = 0 + -13

Combine like terms: 0 + -13 = -13
-1X = -13

Divide each side by '-1'.
X = 13

Simplifying
X = 13
Solution
X = {-1, 13}