0=-2x(3x-1)(4x+3)

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Solution for 0=-2x(3x-1)(4x+3) equation: 


Simplifying
0 = -2x(3x + -1)(4x + 3)

Reorder the terms:
0 = -2x(-1 + 3x)(4x + 3)

Reorder the terms:
0 = -2x(-1 + 3x)(3 + 4x)

Multiply (-1 + 3x) * (3 + 4x)
0 = -2x(-1(3 + 4x) + 3x * (3 + 4x))
0 = -2x((3 * -1 + 4x * -1) + 3x * (3 + 4x))
0 = -2x((-3 + -4x) + 3x * (3 + 4x))
0 = -2x(-3 + -4x + (3 * 3x + 4x * 3x))
0 = -2x(-3 + -4x + (9x + 12x2))

Combine like terms: -4x + 9x = 5x
0 = -2x(-3 + 5x + 12x2)
0 = (-3 * -2x + 5x * -2x + 12x2 * -2x)
0 = (6x + -10x2 + -24x3)

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

Solving for variable 'x'.
Remove the zero:
-6x + 10x2 + 24x3 = 6x + -10x2 + -24x3 + -6x + 10x2 + 24x3

Reorder the terms:
-6x + 10x2 + 24x3 = 6x + -6x + -10x2 + 10x2 + -24x3 + 24x3

Combine like terms: 6x + -6x = 0
-6x + 10x2 + 24x3 = 0 + -10x2 + 10x2 + -24x3 + 24x3
-6x + 10x2 + 24x3 = -10x2 + 10x2 + -24x3 + 24x3

Combine like terms: -10x2 + 10x2 = 0
-6x + 10x2 + 24x3 = 0 + -24x3 + 24x3
-6x + 10x2 + 24x3 = -24x3 + 24x3

Combine like terms: -24x3 + 24x3 = 0
-6x + 10x2 + 24x3 = 0

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

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

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

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

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

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -0.75, 0.3333333333}

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