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Simplifying (3x + -1)(5x + 2) = (3x + -1)(2x + 5) Reorder the terms: (-1 + 3x)(5x + 2) = (3x + -1)(2x + 5) Reorder the terms: (-1 + 3x)(2 + 5x) = (3x + -1)(2x + 5) Multiply (-1 + 3x) * (2 + 5x) (-1(2 + 5x) + 3x * (2 + 5x)) = (3x + -1)(2x + 5) ((2 * -1 + 5x * -1) + 3x * (2 + 5x)) = (3x + -1)(2x + 5) ((-2 + -5x) + 3x * (2 + 5x)) = (3x + -1)(2x + 5) (-2 + -5x + (2 * 3x + 5x * 3x)) = (3x + -1)(2x + 5) (-2 + -5x + (6x + 15x2)) = (3x + -1)(2x + 5) Combine like terms: -5x + 6x = 1x (-2 + 1x + 15x2) = (3x + -1)(2x + 5) Reorder the terms: -2 + 1x + 15x2 = (-1 + 3x)(2x + 5) Reorder the terms: -2 + 1x + 15x2 = (-1 + 3x)(5 + 2x) Multiply (-1 + 3x) * (5 + 2x) -2 + 1x + 15x2 = (-1(5 + 2x) + 3x * (5 + 2x)) -2 + 1x + 15x2 = ((5 * -1 + 2x * -1) + 3x * (5 + 2x)) -2 + 1x + 15x2 = ((-5 + -2x) + 3x * (5 + 2x)) -2 + 1x + 15x2 = (-5 + -2x + (5 * 3x + 2x * 3x)) -2 + 1x + 15x2 = (-5 + -2x + (15x + 6x2)) Combine like terms: -2x + 15x = 13x -2 + 1x + 15x2 = (-5 + 13x + 6x2) Solving -2 + 1x + 15x2 = -5 + 13x + 6x2 Solving for variable 'x'. Reorder the terms: -2 + 5 + 1x + -13x + 15x2 + -6x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2 Combine like terms: -2 + 5 = 3 3 + 1x + -13x + 15x2 + -6x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2 Combine like terms: 1x + -13x = -12x 3 + -12x + 15x2 + -6x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2 Combine like terms: 15x2 + -6x2 = 9x2 3 + -12x + 9x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2 Reorder the terms: 3 + -12x + 9x2 = -5 + 5 + 13x + -13x + 6x2 + -6x2 Combine like terms: -5 + 5 = 0 3 + -12x + 9x2 = 0 + 13x + -13x + 6x2 + -6x2 3 + -12x + 9x2 = 13x + -13x + 6x2 + -6x2 Combine like terms: 13x + -13x = 0 3 + -12x + 9x2 = 0 + 6x2 + -6x2 3 + -12x + 9x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 3 + -12x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -4x + 3x2) = 0 Factor a trinomial. 3((1 + -3x)(1 + -1x)) = 0 Ignore the factor 3.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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.3333333333, 1}
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