2x^3+14x^2=-24x

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Solution for 2x^3+14x^2=-24x equation:


Simplifying
2x3 + 14x2 = -24x

Reorder the terms:
14x2 + 2x3 = -24x

Solving
14x2 + 2x3 = -24x

Solving for variable 'x'.

Reorder the terms:
24x + 14x2 + 2x3 = -24x + 24x

Combine like terms: -24x + 24x = 0
24x + 14x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(12 + 7x + x2) = 0

Factor a trinomial.
2x((4 + x)(3 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 3

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {0, -4, -3}

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