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Simplifying 2x^{2}+ -24x = -2x^{2}+ -7x + -18 Reorder the terms: -24x + 2x^{2}= -2x^{2}+ -7x + -18 Reorder the terms: -24x + 2x^{2}= -18 + -7x + -2x^{2}Solving -24x + 2x^{2}= -18 + -7x + -2x^{2}Solving for variable 'x'. Reorder the terms: 18 + -24x + 7x + 2x^{2}+ 2x^{2}= -18 + -7x + -2x^{2}+ 18 + 7x + 2x^{2}Combine like terms: -24x + 7x = -17x 18 + -17x + 2x^{2}+ 2x^{2}= -18 + -7x + -2x^{2}+ 18 + 7x + 2x^{2}Combine like terms: 2x^{2}+ 2x^{2}= 4x^{2}18 + -17x + 4x^{2}= -18 + -7x + -2x^{2}+ 18 + 7x + 2x^{2}Reorder the terms: 18 + -17x + 4x^{2}= -18 + 18 + -7x + 7x + -2x^{2}+ 2x^{2}Combine like terms: -18 + 18 = 0 18 + -17x + 4x^{2}= 0 + -7x + 7x + -2x^{2}+ 2x^{2}18 + -17x + 4x^{2}= -7x + 7x + -2x^{2}+ 2x^{2}Combine like terms: -7x + 7x = 0 18 + -17x + 4x^{2}= 0 + -2x^{2}+ 2x^{2}18 + -17x + 4x^{2}= -2x^{2}+ 2x^{2}Combine like terms: -2x^{2}+ 2x^{2}= 0 18 + -17x + 4x^{2}= 0 Factor a trinomial. (2 + -1x)(9 + -4x) = 0## Subproblem 1

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

Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25## Solution

x = {2, 2.25}

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