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Simplifying (3x + -1)(4x + 5) = (4x + 5)(2x + -1) Reorder the terms: (-1 + 3x)(4x + 5) = (4x + 5)(2x + -1) Reorder the terms: (-1 + 3x)(5 + 4x) = (4x + 5)(2x + -1) Multiply (-1 + 3x) * (5 + 4x) (-1(5 + 4x) + 3x * (5 + 4x)) = (4x + 5)(2x + -1) ((5 * -1 + 4x * -1) + 3x * (5 + 4x)) = (4x + 5)(2x + -1) ((-5 + -4x) + 3x * (5 + 4x)) = (4x + 5)(2x + -1) (-5 + -4x + (5 * 3x + 4x * 3x)) = (4x + 5)(2x + -1) (-5 + -4x + (15x + 12x2)) = (4x + 5)(2x + -1) Combine like terms: -4x + 15x = 11x (-5 + 11x + 12x2) = (4x + 5)(2x + -1) Reorder the terms: -5 + 11x + 12x2 = (5 + 4x)(2x + -1) Reorder the terms: -5 + 11x + 12x2 = (5 + 4x)(-1 + 2x) Multiply (5 + 4x) * (-1 + 2x) -5 + 11x + 12x2 = (5(-1 + 2x) + 4x * (-1 + 2x)) -5 + 11x + 12x2 = ((-1 * 5 + 2x * 5) + 4x * (-1 + 2x)) -5 + 11x + 12x2 = ((-5 + 10x) + 4x * (-1 + 2x)) -5 + 11x + 12x2 = (-5 + 10x + (-1 * 4x + 2x * 4x)) -5 + 11x + 12x2 = (-5 + 10x + (-4x + 8x2)) Combine like terms: 10x + -4x = 6x -5 + 11x + 12x2 = (-5 + 6x + 8x2) Add '5' to each side of the equation. -5 + 11x + 5 + 12x2 = -5 + 6x + 5 + 8x2 Reorder the terms: -5 + 5 + 11x + 12x2 = -5 + 6x + 5 + 8x2 Combine like terms: -5 + 5 = 0 0 + 11x + 12x2 = -5 + 6x + 5 + 8x2 11x + 12x2 = -5 + 6x + 5 + 8x2 Reorder the terms: 11x + 12x2 = -5 + 5 + 6x + 8x2 Combine like terms: -5 + 5 = 0 11x + 12x2 = 0 + 6x + 8x2 11x + 12x2 = 6x + 8x2 Solving 11x + 12x2 = 6x + 8x2 Solving for variable 'x'. Reorder the terms: 11x + -6x + 12x2 + -8x2 = 6x + 8x2 + -6x + -8x2 Combine like terms: 11x + -6x = 5x 5x + 12x2 + -8x2 = 6x + 8x2 + -6x + -8x2 Combine like terms: 12x2 + -8x2 = 4x2 5x + 4x2 = 6x + 8x2 + -6x + -8x2 Reorder the terms: 5x + 4x2 = 6x + -6x + 8x2 + -8x2 Combine like terms: 6x + -6x = 0 5x + 4x2 = 0 + 8x2 + -8x2 5x + 4x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 5x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 4x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = {0, -1.25}
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