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Simplifying 8a3 = -14a2 + -5a Reorder the terms: 8a3 = -5a + -14a2 Solving 8a3 = -5a + -14a2 Solving for variable 'a'. Reorder the terms: 5a + 14a2 + 8a3 = -5a + -14a2 + 5a + 14a2 Reorder the terms: 5a + 14a2 + 8a3 = -5a + 5a + -14a2 + 14a2 Combine like terms: -5a + 5a = 0 5a + 14a2 + 8a3 = 0 + -14a2 + 14a2 5a + 14a2 + 8a3 = -14a2 + 14a2 Combine like terms: -14a2 + 14a2 = 0 5a + 14a2 + 8a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(5 + 14a + 8a2) = 0 Factor a trinomial. a((5 + 4a)(1 + 2a)) = 0Subproblem 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 '(5 + 4a)' equal to zero and attempt to solve: Simplifying 5 + 4a = 0 Solving 5 + 4a = 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 + 4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4a = 0 + -5 4a = 0 + -5 Combine like terms: 0 + -5 = -5 4a = -5 Divide each side by '4'. a = -1.25 Simplifying a = -1.25Subproblem 3
Set the factor '(1 + 2a)' equal to zero and attempt to solve: Simplifying 1 + 2a = 0 Solving 1 + 2a = 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 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5Solution
a = {0, -1.25, -0.5}
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