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Simplifying 4(a + -2) = 2a(a + 7) Reorder the terms: 4(-2 + a) = 2a(a + 7) (-2 * 4 + a * 4) = 2a(a + 7) (-8 + 4a) = 2a(a + 7) Reorder the terms: -8 + 4a = 2a(7 + a) -8 + 4a = (7 * 2a + a * 2a) -8 + 4a = (14a + 2a2) Solving -8 + 4a = 14a + 2a2 Solving for variable 'a'. Combine like terms: 4a + -14a = -10a -8 + -10a + -2a2 = 14a + 2a2 + -14a + -2a2 Reorder the terms: -8 + -10a + -2a2 = 14a + -14a + 2a2 + -2a2 Combine like terms: 14a + -14a = 0 -8 + -10a + -2a2 = 0 + 2a2 + -2a2 -8 + -10a + -2a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 -8 + -10a + -2a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 5a + a2) = 0 Factor a trinomial. -2((4 + a)(1 + a)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 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 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 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 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {-4, -1}
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