x^3+30x=-13x^2

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Solution for x^3+30x=-13x^2 equation:


Simplifying
x3 + 30x = -13x2

Reorder the terms:
30x + x3 = -13x2

Solving
30x + x3 = -13x2

Solving for variable 'x'.

Reorder the terms:
30x + 13x2 + x3 = -13x2 + 13x2

Combine like terms: -13x2 + 13x2 = 0
30x + 13x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(30 + 13x + x2) = 0

Factor a trinomial.
x((10 + x)(3 + 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10

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, -10, -3}

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