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Simplifying 40 = -5(x + 3)(x + -6) Reorder the terms: 40 = -5(3 + x)(x + -6) Reorder the terms: 40 = -5(3 + x)(-6 + x) Multiply (3 + x) * (-6 + x) 40 = -5(3(-6 + x) + x(-6 + x)) 40 = -5((-6 * 3 + x * 3) + x(-6 + x)) 40 = -5((-18 + 3x) + x(-6 + x)) 40 = -5(-18 + 3x + (-6 * x + x * x)) 40 = -5(-18 + 3x + (-6x + x2)) Combine like terms: 3x + -6x = -3x 40 = -5(-18 + -3x + x2) 40 = (-18 * -5 + -3x * -5 + x2 * -5) 40 = (90 + 15x + -5x2) Solving 40 = 90 + 15x + -5x2 Solving for variable 'x'. Combine like terms: 40 + -90 = -50 -50 + -15x + 5x2 = 90 + 15x + -5x2 + -90 + -15x + 5x2 Reorder the terms: -50 + -15x + 5x2 = 90 + -90 + 15x + -15x + -5x2 + 5x2 Combine like terms: 90 + -90 = 0 -50 + -15x + 5x2 = 0 + 15x + -15x + -5x2 + 5x2 -50 + -15x + 5x2 = 15x + -15x + -5x2 + 5x2 Combine like terms: 15x + -15x = 0 -50 + -15x + 5x2 = 0 + -5x2 + 5x2 -50 + -15x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -50 + -15x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-10 + -3x + x2) = 0 Factor a trinomial. 5((-2 + -1x)(5 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 5Solution
x = {-2, 5}
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