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Simplifying 14a = a3 + -5a2 Reorder the terms: 14a = -5a2 + a3 Solving 14a = -5a2 + a3 Solving for variable 'a'. Reorder the terms: 14a + 5a2 + -1a3 = -5a2 + 5a2 + a3 + -1a3 Combine like terms: -5a2 + 5a2 = 0 14a + 5a2 + -1a3 = 0 + a3 + -1a3 14a + 5a2 + -1a3 = a3 + -1a3 Combine like terms: a3 + -1a3 = 0 14a + 5a2 + -1a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(14 + 5a + -1a2) = 0 Factor a trinomial. a((7 + -1a)(2 + a)) = 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 '(7 + -1a)' equal to zero and attempt to solve: Simplifying 7 + -1a = 0 Solving 7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1a = 0 + -7 -1a = 0 + -7 Combine like terms: 0 + -7 = -7 -1a = -7 Divide each side by '-1'. a = 7 Simplifying a = 7Subproblem 3
Set the factor '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2Solution
a = {0, 7, -2}
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