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

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

Simplifying
(5 + -1x)(x + 4) = 0

Reorder the terms:
(5 + -1x)(4 + x) = 0

Multiply (5 + -1x) * (4 + x)
(5(4 + x) + -1x * (4 + x)) = 0
((4 * 5 + x * 5) + -1x * (4 + x)) = 0
((20 + 5x) + -1x * (4 + x)) = 0
(20 + 5x + (4 * -1x + x * -1x)) = 0
(20 + 5x + (-4x + -1x2)) = 0

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

Solving
20 + 1x + -1x2 = 0

Solving for variable 'x'.

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}