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Simplifying 3x^{2}+ 5x + -13 = 11 + -9x Reorder the terms: -13 + 5x + 3x^{2}= 11 + -9x Solving -13 + 5x + 3x^{2}= 11 + -9x Solving for variable 'x'. Reorder the terms: -13 + -11 + 5x + 9x + 3x^{2}= 11 + -9x + -11 + 9x Combine like terms: -13 + -11 = -24 -24 + 5x + 9x + 3x^{2}= 11 + -9x + -11 + 9x Combine like terms: 5x + 9x = 14x -24 + 14x + 3x^{2}= 11 + -9x + -11 + 9x Reorder the terms: -24 + 14x + 3x^{2}= 11 + -11 + -9x + 9x Combine like terms: 11 + -11 = 0 -24 + 14x + 3x^{2}= 0 + -9x + 9x -24 + 14x + 3x^{2}= -9x + 9x Combine like terms: -9x + 9x = 0 -24 + 14x + 3x^{2}= 0 Factor a trinomial. (-6 + -1x)(4 + -3x) = 0## Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6## Subproblem 2

Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333## Solution

x = {-6, 1.333333333}

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