2x^3+32x=16x^2

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Solution for 2x^3+32x=16x^2 equation:


Simplifying
2x3 + 32x = 16x2

Reorder the terms:
32x + 2x3 = 16x2

Solving
32x + 2x3 = 16x2

Solving for variable 'x'.

Reorder the terms:
32x + -16x2 + 2x3 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
32x + -16x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(16 + -8x + x2) = 0

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

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