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

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


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

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

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

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

Combine like terms: 12x + -2x = 10x
2x(-8 + 10x + 3x2) = 0
(-8 * 2x + 10x * 2x + 3x2 * 2x) = 0
(-16x + 20x2 + 6x3) = 0

Solving
-16x + 20x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + 10x + 3x2) = 0

Factor a trinomial.
2x((-4 + -1x)(2 + -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 '(-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

Subproblem 3
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
Solution
x = {0, -4, 0.6666666667}

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