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Simplifying (4x + -7)(9x + 5) = (8x + -3)(4x + -7) Reorder the terms: (-7 + 4x)(9x + 5) = (8x + -3)(4x + -7) Reorder the terms: (-7 + 4x)(5 + 9x) = (8x + -3)(4x + -7) Multiply (-7 + 4x) * (5 + 9x) (-7(5 + 9x) + 4x * (5 + 9x)) = (8x + -3)(4x + -7) ((5 * -7 + 9x * -7) + 4x * (5 + 9x)) = (8x + -3)(4x + -7) ((-35 + -63x) + 4x * (5 + 9x)) = (8x + -3)(4x + -7) (-35 + -63x + (5 * 4x + 9x * 4x)) = (8x + -3)(4x + -7) (-35 + -63x + (20x + 36x2)) = (8x + -3)(4x + -7) Combine like terms: -63x + 20x = -43x (-35 + -43x + 36x2) = (8x + -3)(4x + -7) Reorder the terms: -35 + -43x + 36x2 = (-3 + 8x)(4x + -7) Reorder the terms: -35 + -43x + 36x2 = (-3 + 8x)(-7 + 4x) Multiply (-3 + 8x) * (-7 + 4x) -35 + -43x + 36x2 = (-3(-7 + 4x) + 8x * (-7 + 4x)) -35 + -43x + 36x2 = ((-7 * -3 + 4x * -3) + 8x * (-7 + 4x)) -35 + -43x + 36x2 = ((21 + -12x) + 8x * (-7 + 4x)) -35 + -43x + 36x2 = (21 + -12x + (-7 * 8x + 4x * 8x)) -35 + -43x + 36x2 = (21 + -12x + (-56x + 32x2)) Combine like terms: -12x + -56x = -68x -35 + -43x + 36x2 = (21 + -68x + 32x2) Solving -35 + -43x + 36x2 = 21 + -68x + 32x2 Solving for variable 'x'. Reorder the terms: -35 + -21 + -43x + 68x + 36x2 + -32x2 = 21 + -68x + 32x2 + -21 + 68x + -32x2 Combine like terms: -35 + -21 = -56 -56 + -43x + 68x + 36x2 + -32x2 = 21 + -68x + 32x2 + -21 + 68x + -32x2 Combine like terms: -43x + 68x = 25x -56 + 25x + 36x2 + -32x2 = 21 + -68x + 32x2 + -21 + 68x + -32x2 Combine like terms: 36x2 + -32x2 = 4x2 -56 + 25x + 4x2 = 21 + -68x + 32x2 + -21 + 68x + -32x2 Reorder the terms: -56 + 25x + 4x2 = 21 + -21 + -68x + 68x + 32x2 + -32x2 Combine like terms: 21 + -21 = 0 -56 + 25x + 4x2 = 0 + -68x + 68x + 32x2 + -32x2 -56 + 25x + 4x2 = -68x + 68x + 32x2 + -32x2 Combine like terms: -68x + 68x = 0 -56 + 25x + 4x2 = 0 + 32x2 + -32x2 -56 + 25x + 4x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 -56 + 25x + 4x2 = 0 Factor a trinomial. (-8 + -1x)(7 + -4x) = 0Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Solution
x = {-8, 1.75}
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