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

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


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

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

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

Multiply (-6 + 3x) * (3 + 6x)
2x(-6(3 + 6x) + 3x * (3 + 6x)) = 0
2x((3 * -6 + 6x * -6) + 3x * (3 + 6x)) = 0
2x((-18 + -36x) + 3x * (3 + 6x)) = 0
2x(-18 + -36x + (3 * 3x + 6x * 3x)) = 0
2x(-18 + -36x + (9x + 18x2)) = 0

Combine like terms: -36x + 9x = -27x
2x(-18 + -27x + 18x2) = 0
(-18 * 2x + -27x * 2x + 18x2 * 2x) = 0
(-36x + -54x2 + 36x3) = 0

Solving
-36x + -54x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18x'.
18x(-2 + -3x + 2x2) = 0

Factor a trinomial.
18x((-1 + -2x)(2 + -1x)) = 0

Ignore the factor 18.

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 '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, -0.5, 2}

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