x^3(x-3)(2x+8)=0

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Solution for x^3(x-3)(2x+8)=0 equation: 


Simplifying
x3(x + -3)(2x + 8) = 0

Reorder the terms:
x3(-3 + x)(2x + 8) = 0

Reorder the terms:
x3(-3 + x)(8 + 2x) = 0

Multiply (-3 + x) * (8 + 2x)
x3(-3(8 + 2x) + x(8 + 2x)) = 0
x3((8 * -3 + 2x * -3) + x(8 + 2x)) = 0
x3((-24 + -6x) + x(8 + 2x)) = 0
x3(-24 + -6x + (8 * x + 2x * x)) = 0
x3(-24 + -6x + (8x + 2x2)) = 0

Combine like terms: -6x + 8x = 2x
x3(-24 + 2x + 2x2) = 0
(-24 * x3 + 2x * x3 + 2x2 * x3) = 0
(-24x3 + 2x4 + 2x5) = 0

Solving
-24x3 + 2x4 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x3'.
2x3(-12 + x + x2) = 0

Factor a trinomial.
2x3((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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 '(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
Solution
x = {-4, 3}

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