x(3x-4)(2x+6)=0

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Solution for x(3x-4)(2x+6)=0 equation: 


Simplifying
x(3x + -4)(2x + 6) = 0

Reorder the terms:
x(-4 + 3x)(2x + 6) = 0

Reorder the terms:
x(-4 + 3x)(6 + 2x) = 0

Multiply (-4 + 3x) * (6 + 2x)
x(-4(6 + 2x) + 3x * (6 + 2x)) = 0
x((6 * -4 + 2x * -4) + 3x * (6 + 2x)) = 0
x((-24 + -8x) + 3x * (6 + 2x)) = 0
x(-24 + -8x + (6 * 3x + 2x * 3x)) = 0
x(-24 + -8x + (18x + 6x2)) = 0

Combine like terms: -8x + 18x = 10x
x(-24 + 10x + 6x2) = 0
(-24 * x + 10x * x + 6x2 * x) = 0
(-24x + 10x2 + 6x3) = 0

Solving
-24x + 10x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-12 + 5x + 3x2) = 0

Factor a trinomial.
2x((-3 + -1x)(4 + -3x)) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -3, 1.333333333}

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