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Simplifying (4a + 4)(3a + 5) = 0 Reorder the terms: (4 + 4a)(3a + 5) = 0 Reorder the terms: (4 + 4a)(5 + 3a) = 0 Multiply (4 + 4a) * (5 + 3a) (4(5 + 3a) + 4a * (5 + 3a)) = 0 ((5 * 4 + 3a * 4) + 4a * (5 + 3a)) = 0 ((20 + 12a) + 4a * (5 + 3a)) = 0 (20 + 12a + (5 * 4a + 3a * 4a)) = 0 (20 + 12a + (20a + 12a2)) = 0 Combine like terms: 12a + 20a = 32a (20 + 32a + 12a2) = 0 Solving 20 + 32a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 8a + 3a2) = 0 Factor a trinomial. 4((5 + 3a)(1 + a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 3a)' equal to zero and attempt to solve: Simplifying 5 + 3a = 0 Solving 5 + 3a = 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 + 3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3a = 0 + -5 3a = 0 + -5 Combine like terms: 0 + -5 = -5 3a = -5 Divide each side by '3'. a = -1.666666667 Simplifying a = -1.666666667Subproblem 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 = {-1.666666667, -1}
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