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Simplifying (x + 3)(x + -9) = 5x + -1 Reorder the terms: (3 + x)(x + -9) = 5x + -1 Reorder the terms: (3 + x)(-9 + x) = 5x + -1 Multiply (3 + x) * (-9 + x) (3(-9 + x) + x(-9 + x)) = 5x + -1 ((-9 * 3 + x * 3) + x(-9 + x)) = 5x + -1 ((-27 + 3x) + x(-9 + x)) = 5x + -1 (-27 + 3x + (-9 * x + x * x)) = 5x + -1 (-27 + 3x + (-9x + x2)) = 5x + -1 Combine like terms: 3x + -9x = -6x (-27 + -6x + x2) = 5x + -1 Reorder the terms: -27 + -6x + x2 = -1 + 5x Solving -27 + -6x + x2 = -1 + 5x Solving for variable 'x'. Reorder the terms: -27 + 1 + -6x + -5x + x2 = -1 + 5x + 1 + -5x Combine like terms: -27 + 1 = -26 -26 + -6x + -5x + x2 = -1 + 5x + 1 + -5x Combine like terms: -6x + -5x = -11x -26 + -11x + x2 = -1 + 5x + 1 + -5x Reorder the terms: -26 + -11x + x2 = -1 + 1 + 5x + -5x Combine like terms: -1 + 1 = 0 -26 + -11x + x2 = 0 + 5x + -5x -26 + -11x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -26 + -11x + x2 = 0 Factor a trinomial. (-2 + -1x)(13 + -1x) = 0Subproblem 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 = -2Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-2, 13}
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