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Simplifying (x + -5)(4x + -3) = (2x + -7)(4x + -3) Reorder the terms: (-5 + x)(4x + -3) = (2x + -7)(4x + -3) Reorder the terms: (-5 + x)(-3 + 4x) = (2x + -7)(4x + -3) Multiply (-5 + x) * (-3 + 4x) (-5(-3 + 4x) + x(-3 + 4x)) = (2x + -7)(4x + -3) ((-3 * -5 + 4x * -5) + x(-3 + 4x)) = (2x + -7)(4x + -3) ((15 + -20x) + x(-3 + 4x)) = (2x + -7)(4x + -3) (15 + -20x + (-3 * x + 4x * x)) = (2x + -7)(4x + -3) (15 + -20x + (-3x + 4x2)) = (2x + -7)(4x + -3) Combine like terms: -20x + -3x = -23x (15 + -23x + 4x2) = (2x + -7)(4x + -3) Reorder the terms: 15 + -23x + 4x2 = (-7 + 2x)(4x + -3) Reorder the terms: 15 + -23x + 4x2 = (-7 + 2x)(-3 + 4x) Multiply (-7 + 2x) * (-3 + 4x) 15 + -23x + 4x2 = (-7(-3 + 4x) + 2x * (-3 + 4x)) 15 + -23x + 4x2 = ((-3 * -7 + 4x * -7) + 2x * (-3 + 4x)) 15 + -23x + 4x2 = ((21 + -28x) + 2x * (-3 + 4x)) 15 + -23x + 4x2 = (21 + -28x + (-3 * 2x + 4x * 2x)) 15 + -23x + 4x2 = (21 + -28x + (-6x + 8x2)) Combine like terms: -28x + -6x = -34x 15 + -23x + 4x2 = (21 + -34x + 8x2) Solving 15 + -23x + 4x2 = 21 + -34x + 8x2 Solving for variable 'x'. Reorder the terms: 15 + -21 + -23x + 34x + 4x2 + -8x2 = 21 + -34x + 8x2 + -21 + 34x + -8x2 Combine like terms: 15 + -21 = -6 -6 + -23x + 34x + 4x2 + -8x2 = 21 + -34x + 8x2 + -21 + 34x + -8x2 Combine like terms: -23x + 34x = 11x -6 + 11x + 4x2 + -8x2 = 21 + -34x + 8x2 + -21 + 34x + -8x2 Combine like terms: 4x2 + -8x2 = -4x2 -6 + 11x + -4x2 = 21 + -34x + 8x2 + -21 + 34x + -8x2 Reorder the terms: -6 + 11x + -4x2 = 21 + -21 + -34x + 34x + 8x2 + -8x2 Combine like terms: 21 + -21 = 0 -6 + 11x + -4x2 = 0 + -34x + 34x + 8x2 + -8x2 -6 + 11x + -4x2 = -34x + 34x + 8x2 + -8x2 Combine like terms: -34x + 34x = 0 -6 + 11x + -4x2 = 0 + 8x2 + -8x2 -6 + 11x + -4x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -6 + 11x + -4x2 = 0 Factor a trinomial. (-2 + x)(3 + -4x) = 0Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {2, 0.75}
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