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Simplifying (9x + -1)(2x + 9) = 0 Reorder the terms: (-1 + 9x)(2x + 9) = 0 Reorder the terms: (-1 + 9x)(9 + 2x) = 0 Multiply (-1 + 9x) * (9 + 2x) (-1(9 + 2x) + 9x * (9 + 2x)) = 0 ((9 * -1 + 2x * -1) + 9x * (9 + 2x)) = 0 ((-9 + -2x) + 9x * (9 + 2x)) = 0 (-9 + -2x + (9 * 9x + 2x * 9x)) = 0 (-9 + -2x + (81x + 18x^{2})) = 0 Combine like terms: -2x + 81x = 79x (-9 + 79x + 18x^{2}) = 0 Solving -9 + 79x + 18x^{2}= 0 Solving for variable 'x'. Factor a trinomial. (-9 + -2x)(1 + -9x) = 0## Subproblem 1

Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 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 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5## Subproblem 2

Set the factor '(1 + -9x)' equal to zero and attempt to solve: Simplifying 1 + -9x = 0 Solving 1 + -9x = 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 + -9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x = 0 + -1 -9x = 0 + -1 Combine like terms: 0 + -1 = -1 -9x = -1 Divide each side by '-9'. x = 0.1111111111 Simplifying x = 0.1111111111## Solution

x = {-4.5, 0.1111111111}

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