x^3=-7x^2-10x

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Solution for x^3=-7x^2-10x equation:


Simplifying
x3 = -7x2 + -10x

Reorder the terms:
x3 = -10x + -7x2

Solving
x3 = -10x + -7x2

Solving for variable 'x'.

Reorder the terms:
10x + 7x2 + x3 = -10x + -7x2 + 10x + 7x2

Reorder the terms:
10x + 7x2 + x3 = -10x + 10x + -7x2 + 7x2

Combine like terms: -10x + 10x = 0
10x + 7x2 + x3 = 0 + -7x2 + 7x2
10x + 7x2 + x3 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
10x + 7x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + 7x + x2) = 0

Factor a trinomial.
x((5 + x)(2 + 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Subproblem 3

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {0, -5, -2}

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