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Simplifying (3x + -1)(x + 5) = (3x + -1)(2x + 4) Reorder the terms: (-1 + 3x)(x + 5) = (3x + -1)(2x + 4) Reorder the terms: (-1 + 3x)(5 + x) = (3x + -1)(2x + 4) Multiply (-1 + 3x) * (5 + x) (-1(5 + x) + 3x * (5 + x)) = (3x + -1)(2x + 4) ((5 * -1 + x * -1) + 3x * (5 + x)) = (3x + -1)(2x + 4) ((-5 + -1x) + 3x * (5 + x)) = (3x + -1)(2x + 4) (-5 + -1x + (5 * 3x + x * 3x)) = (3x + -1)(2x + 4) (-5 + -1x + (15x + 3x2)) = (3x + -1)(2x + 4) Combine like terms: -1x + 15x = 14x (-5 + 14x + 3x2) = (3x + -1)(2x + 4) Reorder the terms: -5 + 14x + 3x2 = (-1 + 3x)(2x + 4) Reorder the terms: -5 + 14x + 3x2 = (-1 + 3x)(4 + 2x) Multiply (-1 + 3x) * (4 + 2x) -5 + 14x + 3x2 = (-1(4 + 2x) + 3x * (4 + 2x)) -5 + 14x + 3x2 = ((4 * -1 + 2x * -1) + 3x * (4 + 2x)) -5 + 14x + 3x2 = ((-4 + -2x) + 3x * (4 + 2x)) -5 + 14x + 3x2 = (-4 + -2x + (4 * 3x + 2x * 3x)) -5 + 14x + 3x2 = (-4 + -2x + (12x + 6x2)) Combine like terms: -2x + 12x = 10x -5 + 14x + 3x2 = (-4 + 10x + 6x2) Solving -5 + 14x + 3x2 = -4 + 10x + 6x2 Solving for variable 'x'. Reorder the terms: -5 + 4 + 14x + -10x + 3x2 + -6x2 = -4 + 10x + 6x2 + 4 + -10x + -6x2 Combine like terms: -5 + 4 = -1 -1 + 14x + -10x + 3x2 + -6x2 = -4 + 10x + 6x2 + 4 + -10x + -6x2 Combine like terms: 14x + -10x = 4x -1 + 4x + 3x2 + -6x2 = -4 + 10x + 6x2 + 4 + -10x + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 -1 + 4x + -3x2 = -4 + 10x + 6x2 + 4 + -10x + -6x2 Reorder the terms: -1 + 4x + -3x2 = -4 + 4 + 10x + -10x + 6x2 + -6x2 Combine like terms: -4 + 4 = 0 -1 + 4x + -3x2 = 0 + 10x + -10x + 6x2 + -6x2 -1 + 4x + -3x2 = 10x + -10x + 6x2 + -6x2 Combine like terms: 10x + -10x = 0 -1 + 4x + -3x2 = 0 + 6x2 + -6x2 -1 + 4x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -1 + 4x + -3x2 = 0 Factor a trinomial. (-1 + x)(1 + -3x) = 0Subproblem 1
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 = 1Subproblem 2
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 = 0.3333333333Solution
x = {1, 0.3333333333}
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