4(5-x)(x+6)=0

Solution for 4(5-x)(x+6)=0 equation:

Simplifying
4(5 + -1x)(x + 6) = 0

Reorder the terms:
4(5 + -1x)(6 + x) = 0

Multiply (5 + -1x) * (6 + x)
4(5(6 + x) + -1x * (6 + x)) = 0
4((6 * 5 + x * 5) + -1x * (6 + x)) = 0
4((30 + 5x) + -1x * (6 + x)) = 0
4(30 + 5x + (6 * -1x + x * -1x)) = 0
4(30 + 5x + (-6x + -1x2)) = 0

Combine like terms: 5x + -6x = -1x
4(30 + -1x + -1x2) = 0
(30 * 4 + -1x * 4 + -1x2 * 4) = 0
(120 + -4x + -4x2) = 0

Solving
120 + -4x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -1x + -1x2) = 0

Factor a trinomial.
4((5 + -1x)(6 + x)) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {5, -6}