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Simplifying a = 5a(3 + -2a) + 7a(a + 4) a = (3 * 5a + -2a * 5a) + 7a(a + 4) a = (15a + -10a2) + 7a(a + 4) Reorder the terms: a = 15a + -10a2 + 7a(4 + a) a = 15a + -10a2 + (4 * 7a + a * 7a) a = 15a + -10a2 + (28a + 7a2) Reorder the terms: a = 15a + 28a + -10a2 + 7a2 Combine like terms: 15a + 28a = 43a a = 43a + -10a2 + 7a2 Combine like terms: -10a2 + 7a2 = -3a2 a = 43a + -3a2 Solving a = 43a + -3a2 Solving for variable 'a'. Combine like terms: a + -43a = -42a -42a + 3a2 = 43a + -3a2 + -43a + 3a2 Reorder the terms: -42a + 3a2 = 43a + -43a + -3a2 + 3a2 Combine like terms: 43a + -43a = 0 -42a + 3a2 = 0 + -3a2 + 3a2 -42a + 3a2 = -3a2 + 3a2 Combine like terms: -3a2 + 3a2 = 0 -42a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3a'. 3a(-14 + a) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-14 + a)' equal to zero and attempt to solve: Simplifying -14 + a = 0 Solving -14 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a = 0 + 14 Combine like terms: -14 + 14 = 0 0 + a = 0 + 14 a = 0 + 14 Combine like terms: 0 + 14 = 14 a = 14 Simplifying a = 14Solution
a = {0, 14}
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