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Simplifying (3 + -1x)(2x + 1) + -1(3 + -1x)(x + -4) = 0 Reorder the terms: (3 + -1x)(1 + 2x) + -1(3 + -1x)(x + -4) = 0 Multiply (3 + -1x) * (1 + 2x) (3(1 + 2x) + -1x * (1 + 2x)) + -1(3 + -1x)(x + -4) = 0 ((1 * 3 + 2x * 3) + -1x * (1 + 2x)) + -1(3 + -1x)(x + -4) = 0 ((3 + 6x) + -1x * (1 + 2x)) + -1(3 + -1x)(x + -4) = 0 (3 + 6x + (1 * -1x + 2x * -1x)) + -1(3 + -1x)(x + -4) = 0 (3 + 6x + (-1x + -2x2)) + -1(3 + -1x)(x + -4) = 0 Combine like terms: 6x + -1x = 5x (3 + 5x + -2x2) + -1(3 + -1x)(x + -4) = 0 Reorder the terms: 3 + 5x + -2x2 + -1(3 + -1x)(-4 + x) = 0 Multiply (3 + -1x) * (-4 + x) 3 + 5x + -2x2 + -1(3(-4 + x) + -1x * (-4 + x)) = 0 3 + 5x + -2x2 + -1((-4 * 3 + x * 3) + -1x * (-4 + x)) = 0 3 + 5x + -2x2 + -1((-12 + 3x) + -1x * (-4 + x)) = 0 3 + 5x + -2x2 + -1(-12 + 3x + (-4 * -1x + x * -1x)) = 0 3 + 5x + -2x2 + -1(-12 + 3x + (4x + -1x2)) = 0 Combine like terms: 3x + 4x = 7x 3 + 5x + -2x2 + -1(-12 + 7x + -1x2) = 0 3 + 5x + -2x2 + (-12 * -1 + 7x * -1 + -1x2 * -1) = 0 3 + 5x + -2x2 + (12 + -7x + 1x2) = 0 Reorder the terms: 3 + 12 + 5x + -7x + -2x2 + 1x2 = 0 Combine like terms: 3 + 12 = 15 15 + 5x + -7x + -2x2 + 1x2 = 0 Combine like terms: 5x + -7x = -2x 15 + -2x + -2x2 + 1x2 = 0 Combine like terms: -2x2 + 1x2 = -1x2 15 + -2x + -1x2 = 0 Solving 15 + -2x + -1x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -1x)(5 + x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {3, -5}
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