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

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


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

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

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

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

Combine like terms: 2x + -12x = -10x
x(-8 + -10x + 3x2) = 0
(-8 * x + -10x * x + 3x2 * x) = 0
(-8x + -10x2 + 3x3) = 0

Solving
-8x + -10x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + -10x + 3x2) = 0

Factor a trinomial.
x((-2 + -3x)(4 + -1x)) = 0


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 '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -0.6666666667, 4}

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