2x^3-64x=28x^2

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Solution for 2x^3-64x=28x^2 equation:


Simplifying
2x3 + -64x = 28x2

Reorder the terms:
-64x + 2x3 = 28x2

Solving
-64x + 2x3 = 28x2

Solving for variable 'x'.

Reorder the terms:
-64x + -28x2 + 2x3 = 28x2 + -28x2

Combine like terms: 28x2 + -28x2 = 0
-64x + -28x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-32 + -14x + x2) = 0

Factor a trinomial.
2x((-2 + -1x)(16 + -1x)) = 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 '(-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 '(16 + -1x)' equal to zero and attempt to solve: Simplifying 16 + -1x = 0 Solving 16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1x = 0 + -16 -1x = 0 + -16 Combine like terms: 0 + -16 = -16 -1x = -16 Divide each side by '-1'. x = 16 Simplifying x = 16

Solution

x = {0, -2, 16}

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