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Simplifying (x + 3)(x + -1) = 2(x + -5)(x + 3) Reorder the terms: (3 + x)(x + -1) = 2(x + -5)(x + 3) Reorder the terms: (3 + x)(-1 + x) = 2(x + -5)(x + 3) Multiply (3 + x) * (-1 + x) (3(-1 + x) + x(-1 + x)) = 2(x + -5)(x + 3) ((-1 * 3 + x * 3) + x(-1 + x)) = 2(x + -5)(x + 3) ((-3 + 3x) + x(-1 + x)) = 2(x + -5)(x + 3) (-3 + 3x + (-1 * x + x * x)) = 2(x + -5)(x + 3) (-3 + 3x + (-1x + x2)) = 2(x + -5)(x + 3) Combine like terms: 3x + -1x = 2x (-3 + 2x + x2) = 2(x + -5)(x + 3) Reorder the terms: -3 + 2x + x2 = 2(-5 + x)(x + 3) Reorder the terms: -3 + 2x + x2 = 2(-5 + x)(3 + x) Multiply (-5 + x) * (3 + x) -3 + 2x + x2 = 2(-5(3 + x) + x(3 + x)) -3 + 2x + x2 = 2((3 * -5 + x * -5) + x(3 + x)) -3 + 2x + x2 = 2((-15 + -5x) + x(3 + x)) -3 + 2x + x2 = 2(-15 + -5x + (3 * x + x * x)) -3 + 2x + x2 = 2(-15 + -5x + (3x + x2)) Combine like terms: -5x + 3x = -2x -3 + 2x + x2 = 2(-15 + -2x + x2) -3 + 2x + x2 = (-15 * 2 + -2x * 2 + x2 * 2) -3 + 2x + x2 = (-30 + -4x + 2x2) Solving -3 + 2x + x2 = -30 + -4x + 2x2 Solving for variable 'x'. Reorder the terms: -3 + 30 + 2x + 4x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2 Combine like terms: -3 + 30 = 27 27 + 2x + 4x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2 Combine like terms: 2x + 4x = 6x 27 + 6x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2 Combine like terms: x2 + -2x2 = -1x2 27 + 6x + -1x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2 Reorder the terms: 27 + 6x + -1x2 = -30 + 30 + -4x + 4x + 2x2 + -2x2 Combine like terms: -30 + 30 = 0 27 + 6x + -1x2 = 0 + -4x + 4x + 2x2 + -2x2 27 + 6x + -1x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 27 + 6x + -1x2 = 0 + 2x2 + -2x2 27 + 6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 27 + 6x + -1x2 = 0 Factor a trinomial. (9 + -1x)(3 + x) = 0Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {9, -3}
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