(x+5)(3x+6)=120

Solution for (x+5)(3x+6)=120 equation:

Simplifying
(x + 5)(3x + 6) = 120

Reorder the terms:
(5 + x)(3x + 6) = 120

Reorder the terms:
(5 + x)(6 + 3x) = 120

Multiply (5 + x) * (6 + 3x)
(5(6 + 3x) + x(6 + 3x)) = 120
((6 * 5 + 3x * 5) + x(6 + 3x)) = 120
((30 + 15x) + x(6 + 3x)) = 120
(30 + 15x + (6 * x + 3x * x)) = 120
(30 + 15x + (6x + 3x2)) = 120

Combine like terms: 15x + 6x = 21x
(30 + 21x + 3x2) = 120

Solving
30 + 21x + 3x2 = 120

Solving for variable 'x'.

Reorder the terms:
30 + -120 + 21x + 3x2 = 120 + -120

Combine like terms: 30 + -120 = -90
-90 + 21x + 3x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-90 + 21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 7x + x2) = 0

Factor a trinomial.
3((-10 + -1x)(3 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-10, 3}