0=(x-5)(x+4)

Solution for 0=(x-5)(x+4) equation:

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

Reorder the terms:
0 = (-5 + x)(x + 4)

Reorder the terms:
0 = (-5 + x)(4 + x)

Multiply (-5 + x) * (4 + x)
0 = (-5(4 + x) + x(4 + x))
0 = ((4 * -5 + x * -5) + x(4 + x))
0 = ((-20 + -5x) + x(4 + x))
0 = (-20 + -5x + (4 * x + x * x))
0 = (-20 + -5x + (4x + x2))

Combine like terms: -5x + 4x = -1x
0 = (-20 + -1x + x2)

Solving
0 = -20 + -1x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(5 + -1x)(4 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {5, -4}