x(3x-9)(4x+2)=0

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Solution for x(3x-9)(4x+2)=0 equation: 


Simplifying
x(3x + -9)(4x + 2) = 0

Reorder the terms:
x(-9 + 3x)(4x + 2) = 0

Reorder the terms:
x(-9 + 3x)(2 + 4x) = 0

Multiply (-9 + 3x) * (2 + 4x)
x(-9(2 + 4x) + 3x * (2 + 4x)) = 0
x((2 * -9 + 4x * -9) + 3x * (2 + 4x)) = 0
x((-18 + -36x) + 3x * (2 + 4x)) = 0
x(-18 + -36x + (2 * 3x + 4x * 3x)) = 0
x(-18 + -36x + (6x + 12x2)) = 0

Combine like terms: -36x + 6x = -30x
x(-18 + -30x + 12x2) = 0
(-18 * x + -30x * x + 12x2 * x) = 0
(-18x + -30x2 + 12x3) = 0

Solving
-18x + -30x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-3 + -5x + 2x2) = 0

Factor a trinomial.
6x((-1 + -2x)(3 + -1x)) = 0

Ignore the factor 6.

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 '(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
Solution
x = {0, -0.5, 3}

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