(x-2)(x+7)=-20

Solution for (x-2)(x+7)=-20 equation:

Simplifying
(x + -2)(x + 7) = -20

Reorder the terms:
(-2 + x)(x + 7) = -20

Reorder the terms:
(-2 + x)(7 + x) = -20

Multiply (-2 + x) * (7 + x)
(-2(7 + x) + x(7 + x)) = -20
((7 * -2 + x * -2) + x(7 + x)) = -20
((-14 + -2x) + x(7 + x)) = -20
(-14 + -2x + (7 * x + x * x)) = -20
(-14 + -2x + (7x + x2)) = -20

Combine like terms: -2x + 7x = 5x
(-14 + 5x + x2) = -20

Solving
-14 + 5x + x2 = -20

Solving for variable 'x'.

Reorder the terms:
-14 + 20 + 5x + x2 = -20 + 20

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

Combine like terms: -20 + 20 = 0
6 + 5x + x2 = 0

Factor a trinomial.
(3 + x)(2 + x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-3, -2}