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Simplifying (3x + -1)(x + 5) + -2(x + 5) = 0 Reorder the terms: (-1 + 3x)(x + 5) + -2(x + 5) = 0 Reorder the terms: (-1 + 3x)(5 + x) + -2(x + 5) = 0 Multiply (-1 + 3x) * (5 + x) (-1(5 + x) + 3x * (5 + x)) + -2(x + 5) = 0 ((5 * -1 + x * -1) + 3x * (5 + x)) + -2(x + 5) = 0 ((-5 + -1x) + 3x * (5 + x)) + -2(x + 5) = 0 (-5 + -1x + (5 * 3x + x * 3x)) + -2(x + 5) = 0 (-5 + -1x + (15x + 3x2)) + -2(x + 5) = 0 Combine like terms: -1x + 15x = 14x (-5 + 14x + 3x2) + -2(x + 5) = 0 Reorder the terms: -5 + 14x + 3x2 + -2(5 + x) = 0 -5 + 14x + 3x2 + (5 * -2 + x * -2) = 0 -5 + 14x + 3x2 + (-10 + -2x) = 0 Reorder the terms: -5 + -10 + 14x + -2x + 3x2 = 0 Combine like terms: -5 + -10 = -15 -15 + 14x + -2x + 3x2 = 0 Combine like terms: 14x + -2x = 12x -15 + 12x + 3x2 = 0 Solving -15 + 12x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 4x + x2) = 0 Factor a trinomial. 3((-5 + -1x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 1}
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