2x^3+3x^2=-x

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


Simplifying
2x3 + 3x2 = -1x

Reorder the terms:
3x2 + 2x3 = -1x

Solving
3x2 + 2x3 = -1x

Solving for variable 'x'.

Reorder the terms:
x + 3x2 + 2x3 = -1x + x

Combine like terms: -1x + x = 0
x + 3x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 3x + 2x2) = 0

Factor a trinomial.
x((1 + x)(1 + 2x)) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Subproblem 3

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {0, -1, -0.5}

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