(3x-3)(x+2)=120

Solution for (3x-3)(x+2)=120 equation:

Simplifying
(3x + -3)(x + 2) = 120

Reorder the terms:
(-3 + 3x)(x + 2) = 120

Reorder the terms:
(-3 + 3x)(2 + x) = 120

Multiply (-3 + 3x) * (2 + x)
(-3(2 + x) + 3x * (2 + x)) = 120
((2 * -3 + x * -3) + 3x * (2 + x)) = 120
((-6 + -3x) + 3x * (2 + x)) = 120
(-6 + -3x + (2 * 3x + x * 3x)) = 120
(-6 + -3x + (6x + 3x2)) = 120

Combine like terms: -3x + 6x = 3x
(-6 + 3x + 3x2) = 120

Solving
-6 + 3x + 3x2 = 120

Solving for variable 'x'.

Reorder the terms:
-6 + -120 + 3x + 3x2 = 120 + -120

Combine like terms: -6 + -120 = -126
-126 + 3x + 3x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-126 + 3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7, 6}