3(x-2)(x-2)=27

Solution for 3(x-2)(x-2)=27 equation:

Simplifying
3(x + -2)(x + -2) = 27

Reorder the terms:
3(-2 + x)(x + -2) = 27

Reorder the terms:
3(-2 + x)(-2 + x) = 27

Multiply (-2 + x) * (-2 + x)
3(-2(-2 + x) + x(-2 + x)) = 27
3((-2 * -2 + x * -2) + x(-2 + x)) = 27
3((4 + -2x) + x(-2 + x)) = 27
3(4 + -2x + (-2 * x + x * x)) = 27
3(4 + -2x + (-2x + x2)) = 27

Combine like terms: -2x + -2x = -4x
3(4 + -4x + x2) = 27
(4 * 3 + -4x * 3 + x2 * 3) = 27
(12 + -12x + 3x2) = 27

Solving
12 + -12x + 3x2 = 27

Solving for variable 'x'.

Reorder the terms:
12 + -27 + -12x + 3x2 = 27 + -27

Combine like terms: 12 + -27 = -15
-15 + -12x + 3x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-15 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -4x + x2) = 0

Factor a trinomial.
3((-1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}