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

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

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

Reorder the terms:
4x2(-6 + x) + 6x(x + -6) = 0
(-6 * 4x2 + x * 4x2) + 6x(x + -6) = 0
(-24x2 + 4x3) + 6x(x + -6) = 0

Reorder the terms:
-24x2 + 4x3 + 6x(-6 + x) = 0
-24x2 + 4x3 + (-6 * 6x + x * 6x) = 0
-24x2 + 4x3 + (-36x + 6x2) = 0

Reorder the terms:
-36x + -24x2 + 6x2 + 4x3 = 0

Combine like terms: -24x2 + 6x2 = -18x2
-36x + -18x2 + 4x3 = 0

Solving
-36x + -18x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-18 + -9x + 2x2) = 0

Factor a trinomial.
2x((-3 + -2x)(6 + -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 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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, -1.5, 6}