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Simplifying (x + 3)(x + -7) = (x + 3)(2x + -2) Reorder the terms: (3 + x)(x + -7) = (x + 3)(2x + -2) Reorder the terms: (3 + x)(-7 + x) = (x + 3)(2x + -2) Multiply (3 + x) * (-7 + x) (3(-7 + x) + x(-7 + x)) = (x + 3)(2x + -2) ((-7 * 3 + x * 3) + x(-7 + x)) = (x + 3)(2x + -2) ((-21 + 3x) + x(-7 + x)) = (x + 3)(2x + -2) (-21 + 3x + (-7 * x + x * x)) = (x + 3)(2x + -2) (-21 + 3x + (-7x + x2)) = (x + 3)(2x + -2) Combine like terms: 3x + -7x = -4x (-21 + -4x + x2) = (x + 3)(2x + -2) Reorder the terms: -21 + -4x + x2 = (3 + x)(2x + -2) Reorder the terms: -21 + -4x + x2 = (3 + x)(-2 + 2x) Multiply (3 + x) * (-2 + 2x) -21 + -4x + x2 = (3(-2 + 2x) + x(-2 + 2x)) -21 + -4x + x2 = ((-2 * 3 + 2x * 3) + x(-2 + 2x)) -21 + -4x + x2 = ((-6 + 6x) + x(-2 + 2x)) -21 + -4x + x2 = (-6 + 6x + (-2 * x + 2x * x)) -21 + -4x + x2 = (-6 + 6x + (-2x + 2x2)) Combine like terms: 6x + -2x = 4x -21 + -4x + x2 = (-6 + 4x + 2x2) Solving -21 + -4x + x2 = -6 + 4x + 2x2 Solving for variable 'x'. Reorder the terms: -21 + 6 + -4x + -4x + x2 + -2x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2 Combine like terms: -21 + 6 = -15 -15 + -4x + -4x + x2 + -2x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2 Combine like terms: -4x + -4x = -8x -15 + -8x + x2 + -2x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -15 + -8x + -1x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2 Reorder the terms: -15 + -8x + -1x2 = -6 + 6 + 4x + -4x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 -15 + -8x + -1x2 = 0 + 4x + -4x + 2x2 + -2x2 -15 + -8x + -1x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -15 + -8x + -1x2 = 0 + 2x2 + -2x2 -15 + -8x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 8x + x2) = 0 Factor a trinomial. -1((5 + x)(3 + x)) = 0 Ignore the factor -1.Subproblem 1
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 = -5Subproblem 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 = {-5, -3}
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