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

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

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

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

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

Multiply (3 + 2x) * (2 + x)
(3(2 + x) + 2x * (2 + x)) = 120
((2 * 3 + x * 3) + 2x * (2 + x)) = 120
((6 + 3x) + 2x * (2 + x)) = 120
(6 + 3x + (2 * 2x + x * 2x)) = 120
(6 + 3x + (4x + 2x2)) = 120

Combine like terms: 3x + 4x = 7x
(6 + 7x + 2x2) = 120

Solving
6 + 7x + 2x2 = 120

Solving for variable 'x'.

Reorder the terms:
6 + -120 + 7x + 2x2 = 120 + -120

Combine like terms: 6 + -120 = -114
-114 + 7x + 2x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-114 + 7x + 2x2 = 0

Factor a trinomial.
(-19 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve:

Simplifying
-19 + -2x = 0

Solving
-19 + -2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x = 0 + 19
-2x = 0 + 19

Combine like terms: 0 + 19 = 19
-2x = 19

Divide each side by '-2'.
x = -9.5

Simplifying
x = -9.5
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 = {-9.5, 6}