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Simplifying -14a2 = 12a3 + -48a Reorder the terms: -14a2 = -48a + 12a3 Solving -14a2 = -48a + 12a3 Solving for variable 'a'. Reorder the terms: 48a + -14a2 + -12a3 = -48a + 12a3 + 48a + -12a3 Reorder the terms: 48a + -14a2 + -12a3 = -48a + 48a + 12a3 + -12a3 Combine like terms: -48a + 48a = 0 48a + -14a2 + -12a3 = 0 + 12a3 + -12a3 48a + -14a2 + -12a3 = 12a3 + -12a3 Combine like terms: 12a3 + -12a3 = 0 48a + -14a2 + -12a3 = 0 Factor out the Greatest Common Factor (GCF), '2a'. 2a(24 + -7a + -6a2) = 0 Factor a trinomial. 2a((3 + -2a)(8 + 3a)) = 0 Ignore the factor 2.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 '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Subproblem 3
Set the factor '(8 + 3a)' equal to zero and attempt to solve: Simplifying 8 + 3a = 0 Solving 8 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3a = 0 + -8 3a = 0 + -8 Combine like terms: 0 + -8 = -8 3a = -8 Divide each side by '3'. a = -2.666666667 Simplifying a = -2.666666667Solution
a = {0, 1.5, -2.666666667}
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