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

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

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

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

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

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

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

Solving
20 + 21x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
20 + -120 + 21x + x2 = 120 + -120

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

Combine like terms: 120 + -120 = 0
-100 + 21x + x2 = 0

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

Subproblem 1
Set the factor '(-25 + -1x)' equal to zero and attempt to solve:

Simplifying
-25 + -1x = 0

Solving
-25 + -1x = 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 + -1x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1x = 0 + 25
-1x = 0 + 25

Combine like terms: 0 + 25 = 25
-1x = 25

Divide each side by '-1'.
x = -25

Simplifying
x = -25
Subproblem 2
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
Solution
x = {-25, 4}