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Simplifying x(5x + 10) = 2x^{2}+ -3x + 30 Reorder the terms: x(10 + 5x) = 2x^{2}+ -3x + 30 (10 * x + 5x * x) = 2x^{2}+ -3x + 30 (10x + 5x^{2}) = 2x^{2}+ -3x + 30 Reorder the terms: 10x + 5x^{2}= 30 + -3x + 2x^{2}Solving 10x + 5x^{2}= 30 + -3x + 2x^{2}Solving for variable 'x'. Reorder the terms: -30 + 10x + 3x + 5x^{2}+ -2x^{2}= 30 + -3x + 2x^{2}+ -30 + 3x + -2x^{2}Combine like terms: 10x + 3x = 13x -30 + 13x + 5x^{2}+ -2x^{2}= 30 + -3x + 2x^{2}+ -30 + 3x + -2x^{2}Combine like terms: 5x^{2}+ -2x^{2}= 3x^{2}-30 + 13x + 3x^{2}= 30 + -3x + 2x^{2}+ -30 + 3x + -2x^{2}Reorder the terms: -30 + 13x + 3x^{2}= 30 + -30 + -3x + 3x + 2x^{2}+ -2x^{2}Combine like terms: 30 + -30 = 0 -30 + 13x + 3x^{2}= 0 + -3x + 3x + 2x^{2}+ -2x^{2}-30 + 13x + 3x^{2}= -3x + 3x + 2x^{2}+ -2x^{2}Combine like terms: -3x + 3x = 0 -30 + 13x + 3x^{2}= 0 + 2x^{2}+ -2x^{2}-30 + 13x + 3x^{2}= 2x^{2}+ -2x^{2}Combine like terms: 2x^{2}+ -2x^{2}= 0 -30 + 13x + 3x^{2}= 0 Factor a trinomial. (-6 + -1x)(5 + -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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667## Solution

x = {-6, 1.666666667}

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