(x+2)(x+3)=20

Solution for (x+2)(x+3)=20 equation:

Simplifying
(x + 2)(x + 3) = 20

Reorder the terms:
(2 + x)(x + 3) = 20

Reorder the terms:
(2 + x)(3 + x) = 20

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 20
((3 * 2 + x * 2) + x(3 + x)) = 20
((6 + 2x) + x(3 + x)) = 20
(6 + 2x + (3 * x + x * x)) = 20
(6 + 2x + (3x + x2)) = 20

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 20

Solving
6 + 5x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
6 + -20 + 5x + x2 = 20 + -20

Combine like terms: 6 + -20 = -14
-14 + 5x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-14 + 5x + x2 = 0

Factor a trinomial.
(-7 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-7, 2}