(3x+3)(x)=126

Solution for (3x+3)(x)=126 equation:

Simplifying
(3x + 3)(x) = 126

Reorder the terms:
(3 + 3x)(x) = 126

Reorder the terms for easier multiplication:
x(3 + 3x) = 126
(3 * x + 3x * x) = 126
(3x + 3x2) = 126

Solving
3x + 3x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 3x + 3x2 = 126 + -126

Combine like terms: 126 + -126 = 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}