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

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

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

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

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

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

Combine like terms: -5x + 6x = 1x
4x(-30 + 1x + x2) = 0
(-30 * 4x + 1x * 4x + x2 * 4x) = 0
(-120x + 4x2 + 4x3) = 0

Solving
-120x + 4x2 + 4x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
4x((-6 + -1x)(5 + -1x)) = 0

Ignore the factor 4.
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 '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 3
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
Solution
x = {0, -6, 5}