(x+1)(x+2)-20=0

Solution for (x+1)(x+2)-20=0 equation:

Simplifying
(x + 1)(x + 2) + -20 = 0

Reorder the terms:
(1 + x)(x + 2) + -20 = 0

Reorder the terms:
(1 + x)(2 + x) + -20 = 0

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) + -20 = 0
((2 * 1 + x * 1) + x(2 + x)) + -20 = 0
((2 + 1x) + x(2 + x)) + -20 = 0
(2 + 1x + (2 * x + x * x)) + -20 = 0
(2 + 1x + (2x + x2)) + -20 = 0

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) + -20 = 0

Reorder the terms:
2 + -20 + 3x + x2 = 0

Combine like terms: 2 + -20 = -18
-18 + 3x + x2 = 0

Solving
-18 + 3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0

Subproblem 1
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
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 = {-6, 3}