(4x-16)(x+5)=0

Solution for (4x-16)(x+5)=0 equation:

Simplifying
(4x + -16)(x + 5) = 0

Reorder the terms:
(-16 + 4x)(x + 5) = 0

Reorder the terms:
(-16 + 4x)(5 + x) = 0

Multiply (-16 + 4x) * (5 + x)
(-16(5 + x) + 4x * (5 + x)) = 0
((5 * -16 + x * -16) + 4x * (5 + x)) = 0
((-80 + -16x) + 4x * (5 + x)) = 0
(-80 + -16x + (5 * 4x + x * 4x)) = 0
(-80 + -16x + (20x + 4x2)) = 0

Combine like terms: -16x + 20x = 4x
(-80 + 4x + 4x2) = 0

Solving
-80 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + x + x2) = 0

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

Ignore the factor 4.
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 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

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