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Simplifying (x + 9)(4x + -5) = (x + -17)(1 + -3x) Reorder the terms: (9 + x)(4x + -5) = (x + -17)(1 + -3x) Reorder the terms: (9 + x)(-5 + 4x) = (x + -17)(1 + -3x) Multiply (9 + x) * (-5 + 4x) (9(-5 + 4x) + x(-5 + 4x)) = (x + -17)(1 + -3x) ((-5 * 9 + 4x * 9) + x(-5 + 4x)) = (x + -17)(1 + -3x) ((-45 + 36x) + x(-5 + 4x)) = (x + -17)(1 + -3x) (-45 + 36x + (-5 * x + 4x * x)) = (x + -17)(1 + -3x) (-45 + 36x + (-5x + 4x2)) = (x + -17)(1 + -3x) Combine like terms: 36x + -5x = 31x (-45 + 31x + 4x2) = (x + -17)(1 + -3x) Reorder the terms: -45 + 31x + 4x2 = (-17 + x)(1 + -3x) Multiply (-17 + x) * (1 + -3x) -45 + 31x + 4x2 = (-17(1 + -3x) + x(1 + -3x)) -45 + 31x + 4x2 = ((1 * -17 + -3x * -17) + x(1 + -3x)) -45 + 31x + 4x2 = ((-17 + 51x) + x(1 + -3x)) -45 + 31x + 4x2 = (-17 + 51x + (1 * x + -3x * x)) -45 + 31x + 4x2 = (-17 + 51x + (1x + -3x2)) Combine like terms: 51x + 1x = 52x -45 + 31x + 4x2 = (-17 + 52x + -3x2) Solving -45 + 31x + 4x2 = -17 + 52x + -3x2 Solving for variable 'x'. Reorder the terms: -45 + 17 + 31x + -52x + 4x2 + 3x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2 Combine like terms: -45 + 17 = -28 -28 + 31x + -52x + 4x2 + 3x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2 Combine like terms: 31x + -52x = -21x -28 + -21x + 4x2 + 3x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2 Combine like terms: 4x2 + 3x2 = 7x2 -28 + -21x + 7x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2 Reorder the terms: -28 + -21x + 7x2 = -17 + 17 + 52x + -52x + -3x2 + 3x2 Combine like terms: -17 + 17 = 0 -28 + -21x + 7x2 = 0 + 52x + -52x + -3x2 + 3x2 -28 + -21x + 7x2 = 52x + -52x + -3x2 + 3x2 Combine like terms: 52x + -52x = 0 -28 + -21x + 7x2 = 0 + -3x2 + 3x2 -28 + -21x + 7x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -28 + -21x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-4 + -3x + x2) = 0 Factor a trinomial. 7((-1 + -1x)(4 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-1, 4}
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