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Simplifying (3x + 1)(4x + -5) = (3x + 1)(2x + -1) Reorder the terms: (1 + 3x)(4x + -5) = (3x + 1)(2x + -1) Reorder the terms: (1 + 3x)(-5 + 4x) = (3x + 1)(2x + -1) Multiply (1 + 3x) * (-5 + 4x) (1(-5 + 4x) + 3x * (-5 + 4x)) = (3x + 1)(2x + -1) ((-5 * 1 + 4x * 1) + 3x * (-5 + 4x)) = (3x + 1)(2x + -1) ((-5 + 4x) + 3x * (-5 + 4x)) = (3x + 1)(2x + -1) (-5 + 4x + (-5 * 3x + 4x * 3x)) = (3x + 1)(2x + -1) (-5 + 4x + (-15x + 12x2)) = (3x + 1)(2x + -1) Combine like terms: 4x + -15x = -11x (-5 + -11x + 12x2) = (3x + 1)(2x + -1) Reorder the terms: -5 + -11x + 12x2 = (1 + 3x)(2x + -1) Reorder the terms: -5 + -11x + 12x2 = (1 + 3x)(-1 + 2x) Multiply (1 + 3x) * (-1 + 2x) -5 + -11x + 12x2 = (1(-1 + 2x) + 3x * (-1 + 2x)) -5 + -11x + 12x2 = ((-1 * 1 + 2x * 1) + 3x * (-1 + 2x)) -5 + -11x + 12x2 = ((-1 + 2x) + 3x * (-1 + 2x)) -5 + -11x + 12x2 = (-1 + 2x + (-1 * 3x + 2x * 3x)) -5 + -11x + 12x2 = (-1 + 2x + (-3x + 6x2)) Combine like terms: 2x + -3x = -1x -5 + -11x + 12x2 = (-1 + -1x + 6x2) Solving -5 + -11x + 12x2 = -1 + -1x + 6x2 Solving for variable 'x'. Reorder the terms: -5 + 1 + -11x + x + 12x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Combine like terms: -5 + 1 = -4 -4 + -11x + x + 12x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Combine like terms: -11x + x = -10x -4 + -10x + 12x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Combine like terms: 12x2 + -6x2 = 6x2 -4 + -10x + 6x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Reorder the terms: -4 + -10x + 6x2 = -1 + 1 + -1x + x + 6x2 + -6x2 Combine like terms: -1 + 1 = 0 -4 + -10x + 6x2 = 0 + -1x + x + 6x2 + -6x2 -4 + -10x + 6x2 = -1x + x + 6x2 + -6x2 Combine like terms: -1x + x = 0 -4 + -10x + 6x2 = 0 + 6x2 + -6x2 -4 + -10x + 6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + -10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -5x + 3x2) = 0 Factor a trinomial. 2((-1 + -3x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
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 = 2Solution
x = {-0.3333333333, 2}
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