(x-4)*(x+5)=-20

Solution for (x-4)*(x+5)=-20 equation:

Simplifying
(x + -4)(x + 5) = -20

Reorder the terms:
(-4 + x)(x + 5) = -20

Reorder the terms:
(-4 + x)(5 + x) = -20

Multiply (-4 + x) * (5 + x)
(-4(5 + x) + x(5 + x)) = -20
((5 * -4 + x * -4) + x(5 + x)) = -20
((-20 + -4x) + x(5 + x)) = -20
(-20 + -4x + (5 * x + x * x)) = -20
(-20 + -4x + (5x + x2)) = -20

Combine like terms: -4x + 5x = 1x
(-20 + 1x + x2) = -20

Add '20' to each side of the equation.
-20 + 1x + 20 + x2 = -20 + 20

Reorder the terms:
-20 + 20 + 1x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
0 + 1x + x2 = -20 + 20
1x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
1x + x2 = 0

Solving
1x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {0, -1}