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Simplifying [2a + -8][a + 5] = 0 Reorder the terms: [-8 + 2a][a + 5] = 0 Reorder the terms: [-8 + 2a][5 + a] = 0 Multiply [-8 + 2a] * [5 + a] [-8[5 + a] + 2a * [5 + a]] = 0 [[5 * -8 + a * -8] + 2a * [5 + a]] = 0 [[-40 + -8a] + 2a * [5 + a]] = 0 [-40 + -8a + [5 * 2a + a * 2a]] = 0 [-40 + -8a + [10a + 2a2]] = 0 Combine like terms: -8a + 10a = 2a [-40 + 2a + 2a2] = 0 Solving -40 + 2a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + a + a2) = 0 Factor a trinomial. 2((-5 + -1a)(4 + -1a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve: Simplifying -5 + -1a = 0 Solving -5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1a = 0 + 5 -1a = 0 + 5 Combine like terms: 0 + 5 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Solution
a = {-5, 4}
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