(x+5)(x-7)=-20

Solution for (x+5)(x-7)=-20 equation:

Simplifying
(x + 5)(x + -7) = -20

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

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

Multiply (5 + x) * (-7 + x)
(5(-7 + x) + x(-7 + x)) = -20
((-7 * 5 + x * 5) + x(-7 + x)) = -20
((-35 + 5x) + x(-7 + x)) = -20
(-35 + 5x + (-7 * x + x * x)) = -20
(-35 + 5x + (-7x + x2)) = -20

Combine like terms: 5x + -7x = -2x
(-35 + -2x + x2) = -20

Solving
-35 + -2x + x2 = -20

Solving for variable 'x'.

Reorder the terms:
-35 + 20 + -2x + x2 = -20 + 20

Combine like terms: -35 + 20 = -15
-15 + -2x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}