x(2x-3)(x+6)=0

Solution for x(2x-3)(x+6)=0 equation:

Simplifying
x(2x + -3)(x + 6) = 0

Reorder the terms:
x(-3 + 2x)(x + 6) = 0

Reorder the terms:
x(-3 + 2x)(6 + x) = 0

Multiply (-3 + 2x) * (6 + x)
x(-3(6 + x) + 2x * (6 + x)) = 0
x((6 * -3 + x * -3) + 2x * (6 + x)) = 0
x((-18 + -3x) + 2x * (6 + x)) = 0
x(-18 + -3x + (6 * 2x + x * 2x)) = 0
x(-18 + -3x + (12x + 2x2)) = 0

Combine like terms: -3x + 12x = 9x
x(-18 + 9x + 2x2) = 0
(-18 * x + 9x * x + 2x2 * x) = 0
(-18x + 9x2 + 2x3) = 0

Solving
-18x + 9x2 + 2x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((-6 + -1x)(3 + -2x)) = 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 '(-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 '(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
Solution
x = {0, -6, 1.5}