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Simplifying (3x + -4)(x + -8) = (x + -6)(4x + -5) Reorder the terms: (-4 + 3x)(x + -8) = (x + -6)(4x + -5) Reorder the terms: (-4 + 3x)(-8 + x) = (x + -6)(4x + -5) Multiply (-4 + 3x) * (-8 + x) (-4(-8 + x) + 3x * (-8 + x)) = (x + -6)(4x + -5) ((-8 * -4 + x * -4) + 3x * (-8 + x)) = (x + -6)(4x + -5) ((32 + -4x) + 3x * (-8 + x)) = (x + -6)(4x + -5) (32 + -4x + (-8 * 3x + x * 3x)) = (x + -6)(4x + -5) (32 + -4x + (-24x + 3x2)) = (x + -6)(4x + -5) Combine like terms: -4x + -24x = -28x (32 + -28x + 3x2) = (x + -6)(4x + -5) Reorder the terms: 32 + -28x + 3x2 = (-6 + x)(4x + -5) Reorder the terms: 32 + -28x + 3x2 = (-6 + x)(-5 + 4x) Multiply (-6 + x) * (-5 + 4x) 32 + -28x + 3x2 = (-6(-5 + 4x) + x(-5 + 4x)) 32 + -28x + 3x2 = ((-5 * -6 + 4x * -6) + x(-5 + 4x)) 32 + -28x + 3x2 = ((30 + -24x) + x(-5 + 4x)) 32 + -28x + 3x2 = (30 + -24x + (-5 * x + 4x * x)) 32 + -28x + 3x2 = (30 + -24x + (-5x + 4x2)) Combine like terms: -24x + -5x = -29x 32 + -28x + 3x2 = (30 + -29x + 4x2) Solving 32 + -28x + 3x2 = 30 + -29x + 4x2 Solving for variable 'x'. Reorder the terms: 32 + -30 + -28x + 29x + 3x2 + -4x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2 Combine like terms: 32 + -30 = 2 2 + -28x + 29x + 3x2 + -4x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2 Combine like terms: -28x + 29x = 1x 2 + 1x + 3x2 + -4x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 2 + 1x + -1x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2 Reorder the terms: 2 + 1x + -1x2 = 30 + -30 + -29x + 29x + 4x2 + -4x2 Combine like terms: 30 + -30 = 0 2 + 1x + -1x2 = 0 + -29x + 29x + 4x2 + -4x2 2 + 1x + -1x2 = -29x + 29x + 4x2 + -4x2 Combine like terms: -29x + 29x = 0 2 + 1x + -1x2 = 0 + 4x2 + -4x2 2 + 1x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2 + 1x + -1x2 = 0 Factor a trinomial. (2 + -1x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {2, -1}
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