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

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

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

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

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

Solving
120 = 60 + 17x + x2

Solving for variable 'x'.

Combine like terms: 120 + -60 = 60
60 + -17x + -1x2 = 60 + 17x + x2 + -60 + -17x + -1x2

Reorder the terms:
60 + -17x + -1x2 = 60 + -60 + 17x + -17x + x2 + -1x2

Combine like terms: 60 + -60 = 0
60 + -17x + -1x2 = 0 + 17x + -17x + x2 + -1x2
60 + -17x + -1x2 = 17x + -17x + x2 + -1x2

Combine like terms: 17x + -17x = 0
60 + -17x + -1x2 = 0 + x2 + -1x2
60 + -17x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + -17x + -1x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 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 + x = 0 + -20

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

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

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