(3x+3)(x-2)=54

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Solution for (3x+3)(x-2)=54 equation: 


Simplifying
(3x + 3)(x + -2) = 54

Reorder the terms:
(3 + 3x)(x + -2) = 54

Reorder the terms:
(3 + 3x)(-2 + x) = 54

Multiply (3 + 3x) * (-2 + x)
(3(-2 + x) + 3x * (-2 + x)) = 54
((-2 * 3 + x * 3) + 3x * (-2 + x)) = 54
((-6 + 3x) + 3x * (-2 + x)) = 54
(-6 + 3x + (-2 * 3x + x * 3x)) = 54
(-6 + 3x + (-6x + 3x2)) = 54

Combine like terms: 3x + -6x = -3x
(-6 + -3x + 3x2) = 54

Solving
-6 + -3x + 3x2 = 54

Solving for variable 'x'.

Reorder the terms:
-6 + -54 + -3x + 3x2 = 54 + -54

Combine like terms: -6 + -54 = -60
-60 + -3x + 3x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-60 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -1x + x2) = 0

Factor a trinomial.
3((-4 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 5}

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