x^3=2x^2+8x

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Solution for x^3=2x^2+8x equation:


Simplifying
x3 = 2x2 + 8x

Reorder the terms:
x3 = 8x + 2x2

Solving
x3 = 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8x + -2x2 + x3 = 8x + 2x2 + -8x + -2x2

Reorder the terms:
-8x + -2x2 + x3 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
-8x + -2x2 + x3 = 0 + 2x2 + -2x2
-8x + -2x2 + x3 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8x + -2x2 + x3 = 0

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

Factor a trinomial.
x((-2 + -1x)(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 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

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, -2, 4}

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