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Simplifying 3a(a + 4) + -1(a + 4) = 2(a + 4) Reorder the terms: 3a(4 + a) + -1(a + 4) = 2(a + 4) (4 * 3a + a * 3a) + -1(a + 4) = 2(a + 4) (12a + 3a2) + -1(a + 4) = 2(a + 4) Reorder the terms: 12a + 3a2 + -1(4 + a) = 2(a + 4) 12a + 3a2 + (4 * -1 + a * -1) = 2(a + 4) 12a + 3a2 + (-4 + -1a) = 2(a + 4) Reorder the terms: -4 + 12a + -1a + 3a2 = 2(a + 4) Combine like terms: 12a + -1a = 11a -4 + 11a + 3a2 = 2(a + 4) Reorder the terms: -4 + 11a + 3a2 = 2(4 + a) -4 + 11a + 3a2 = (4 * 2 + a * 2) -4 + 11a + 3a2 = (8 + 2a) Solving -4 + 11a + 3a2 = 8 + 2a Solving for variable 'a'. Reorder the terms: -4 + -8 + 11a + -2a + 3a2 = 8 + 2a + -8 + -2a Combine like terms: -4 + -8 = -12 -12 + 11a + -2a + 3a2 = 8 + 2a + -8 + -2a Combine like terms: 11a + -2a = 9a -12 + 9a + 3a2 = 8 + 2a + -8 + -2a Reorder the terms: -12 + 9a + 3a2 = 8 + -8 + 2a + -2a Combine like terms: 8 + -8 = 0 -12 + 9a + 3a2 = 0 + 2a + -2a -12 + 9a + 3a2 = 2a + -2a Combine like terms: 2a + -2a = 0 -12 + 9a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 3a + a2) = 0 Factor a trinomial. 3((-4 + -1a)(1 + -1a)) = 0 Ignore the factor 3.Subproblem 1
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 = -4Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {-4, 1}
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