x^3=-10x^2-24x

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Solution for x^3=-10x^2-24x equation:


Simplifying
x3 = -10x2 + -24x

Reorder the terms:
x3 = -24x + -10x2

Solving
x3 = -24x + -10x2

Solving for variable 'x'.

Reorder the terms:
24x + 10x2 + x3 = -24x + -10x2 + 24x + 10x2

Reorder the terms:
24x + 10x2 + x3 = -24x + 24x + -10x2 + 10x2

Combine like terms: -24x + 24x = 0
24x + 10x2 + x3 = 0 + -10x2 + 10x2
24x + 10x2 + x3 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
24x + 10x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(24 + 10x + x2) = 0

Factor a trinomial.
x((6 + x)(4 + x)) = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Subproblem 3

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

Solution

x = {0, -6, -4}

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