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Simplifying 20x^{3}+ 13x^{2}+ 2x = 0 Reorder the terms: 2x + 13x^{2}+ 20x^{3}= 0 Solving 2x + 13x^{2}+ 20x^{3}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + 13x + 20x^{2}) = 0 Factor a trinomial. x((2 + 5x)(1 + 4x)) = 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 '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 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 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4## Subproblem 3

Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25## Solution

x = {0, -0.4, -0.25}

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