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

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


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

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

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

Multiply (-3 + 2x) * (4 + x)
-3x(-3(4 + x) + 2x * (4 + x)) = 0
-3x((4 * -3 + x * -3) + 2x * (4 + x)) = 0
-3x((-12 + -3x) + 2x * (4 + x)) = 0
-3x(-12 + -3x + (4 * 2x + x * 2x)) = 0
-3x(-12 + -3x + (8x + 2x2)) = 0

Combine like terms: -3x + 8x = 5x
-3x(-12 + 5x + 2x2) = 0
(-12 * -3x + 5x * -3x + 2x2 * -3x) = 0
(36x + -15x2 + -6x3) = 0

Solving
36x + -15x2 + -6x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
3x((3 + -2x)(4 + x)) = 0

Ignore the factor 3.

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 + -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

Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {0, 1.5, -4}

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