120=(x+1)(x+20)

Solution for 120=(x+1)(x+20) equation:

Simplifying
120 = (x + 1)(x + 20)

Reorder the terms:
120 = (1 + x)(x + 20)

Reorder the terms:
120 = (1 + x)(20 + x)

Multiply (1 + x) * (20 + x)
120 = (1(20 + x) + x(20 + x))
120 = ((20 * 1 + x * 1) + x(20 + x))
120 = ((20 + 1x) + x(20 + x))
120 = (20 + 1x + (20 * x + x * x))
120 = (20 + 1x + (20x + x2))

Combine like terms: 1x + 20x = 21x
120 = (20 + 21x + x2)

Solving
120 = 20 + 21x + x2

Solving for variable 'x'.

Combine like terms: 120 + -20 = 100
100 + -21x + -1x2 = 20 + 21x + x2 + -20 + -21x + -1x2

Reorder the terms:
100 + -21x + -1x2 = 20 + -20 + 21x + -21x + x2 + -1x2

Combine like terms: 20 + -20 = 0
100 + -21x + -1x2 = 0 + 21x + -21x + x2 + -1x2
100 + -21x + -1x2 = 21x + -21x + x2 + -1x2

Combine like terms: 21x + -21x = 0
100 + -21x + -1x2 = 0 + x2 + -1x2
100 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
100 + -21x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(25 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

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

Add '-25' to each side of the equation.
25 + -25 + x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x = 0 + -25
x = 0 + -25

Combine like terms: 0 + -25 = -25
x = -25

Simplifying
x = -25
Solution
x = {4, -25}