(5+x)(12+x)=120

Solution for (5+x)(12+x)=120 equation:

Simplifying
(5 + x)(12 + x) = 120

Multiply (5 + x) * (12 + x)
(5(12 + x) + x(12 + x)) = 120
((12 * 5 + x * 5) + x(12 + x)) = 120
((60 + 5x) + x(12 + x)) = 120
(60 + 5x + (12 * x + x * x)) = 120
(60 + 5x + (12x + x2)) = 120

Combine like terms: 5x + 12x = 17x
(60 + 17x + x2) = 120

Solving
60 + 17x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
60 + -120 + 17x + x2 = 120 + -120

Combine like terms: 60 + -120 = -60
-60 + 17x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-60 + 17x + x2 = 0

Factor a trinomial.
(-20 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
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 = {-20, 3}