(x-6)(x^2+4x)=0

Solution for (x-6)(x^2+4x)=0 equation:

Simplifying
(x + -6)(x2 + 4x) = 0

Reorder the terms:
(-6 + x)(x2 + 4x) = 0

Reorder the terms:
(-6 + x)(4x + x2) = 0

Multiply (-6 + x) * (4x + x2)
(-6(4x + x2) + x(4x + x2)) = 0
((4x * -6 + x2 * -6) + x(4x + x2)) = 0
((-24x + -6x2) + x(4x + x2)) = 0
(-24x + -6x2 + (4x * x + x2 * x)) = 0
(-24x + -6x2 + (4x2 + x3)) = 0

Combine like terms: -6x2 + 4x2 = -2x2
(-24x + -2x2 + x3) = 0

Solving
-24x + -2x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + -2x + x2) = 0

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

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 '(-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
Subproblem 3
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
Solution
x = {0, -4, 6}