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Simplifying (4x + -5)(5x + 7) = (4x + -5)(4x + 5) Reorder the terms: (-5 + 4x)(5x + 7) = (4x + -5)(4x + 5) Reorder the terms: (-5 + 4x)(7 + 5x) = (4x + -5)(4x + 5) Multiply (-5 + 4x) * (7 + 5x) (-5(7 + 5x) + 4x * (7 + 5x)) = (4x + -5)(4x + 5) ((7 * -5 + 5x * -5) + 4x * (7 + 5x)) = (4x + -5)(4x + 5) ((-35 + -25x) + 4x * (7 + 5x)) = (4x + -5)(4x + 5) (-35 + -25x + (7 * 4x + 5x * 4x)) = (4x + -5)(4x + 5) (-35 + -25x + (28x + 20x2)) = (4x + -5)(4x + 5) Combine like terms: -25x + 28x = 3x (-35 + 3x + 20x2) = (4x + -5)(4x + 5) Reorder the terms: -35 + 3x + 20x2 = (-5 + 4x)(4x + 5) Reorder the terms: -35 + 3x + 20x2 = (-5 + 4x)(5 + 4x) Multiply (-5 + 4x) * (5 + 4x) -35 + 3x + 20x2 = (-5(5 + 4x) + 4x * (5 + 4x)) -35 + 3x + 20x2 = ((5 * -5 + 4x * -5) + 4x * (5 + 4x)) -35 + 3x + 20x2 = ((-25 + -20x) + 4x * (5 + 4x)) -35 + 3x + 20x2 = (-25 + -20x + (5 * 4x + 4x * 4x)) -35 + 3x + 20x2 = (-25 + -20x + (20x + 16x2)) Combine like terms: -20x + 20x = 0 -35 + 3x + 20x2 = (-25 + 0 + 16x2) -35 + 3x + 20x2 = (-25 + 16x2) Solving -35 + 3x + 20x2 = -25 + 16x2 Solving for variable 'x'. Reorder the terms: -35 + 25 + 3x + 20x2 + -16x2 = -25 + 16x2 + 25 + -16x2 Combine like terms: -35 + 25 = -10 -10 + 3x + 20x2 + -16x2 = -25 + 16x2 + 25 + -16x2 Combine like terms: 20x2 + -16x2 = 4x2 -10 + 3x + 4x2 = -25 + 16x2 + 25 + -16x2 Reorder the terms: -10 + 3x + 4x2 = -25 + 25 + 16x2 + -16x2 Combine like terms: -25 + 25 = 0 -10 + 3x + 4x2 = 0 + 16x2 + -16x2 -10 + 3x + 4x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -10 + 3x + 4x2 = 0 Factor a trinomial. (-2 + -1x)(5 + -4x) = 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 '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Solution
x = {-2, 1.25}
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