x(6+2x)(x-5)=0

Solution for x(6+2x)(x-5)=0 equation:

Simplifying
x(6 + 2x)(x + -5) = 0

Reorder the terms:
x(6 + 2x)(-5 + x) = 0

Multiply (6 + 2x) * (-5 + x)
x(6(-5 + x) + 2x * (-5 + x)) = 0
x((-5 * 6 + x * 6) + 2x * (-5 + x)) = 0
x((-30 + 6x) + 2x * (-5 + x)) = 0
x(-30 + 6x + (-5 * 2x + x * 2x)) = 0
x(-30 + 6x + (-10x + 2x2)) = 0

Combine like terms: 6x + -10x = -4x
x(-30 + -4x + 2x2) = 0
(-30 * x + -4x * x + 2x2 * x) = 0
(-30x + -4x2 + 2x3) = 0

Solving
-30x + -4x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-15 + -2x + x2) = 0

Factor a trinomial.
2x((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
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 '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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, -3, 5}