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Simplifying 12a3 = -17a2 + -6a Reorder the terms: 12a3 = -6a + -17a2 Solving 12a3 = -6a + -17a2 Solving for variable 'a'. Reorder the terms: 6a + 17a2 + 12a3 = -6a + -17a2 + 6a + 17a2 Reorder the terms: 6a + 17a2 + 12a3 = -6a + 6a + -17a2 + 17a2 Combine like terms: -6a + 6a = 0 6a + 17a2 + 12a3 = 0 + -17a2 + 17a2 6a + 17a2 + 12a3 = -17a2 + 17a2 Combine like terms: -17a2 + 17a2 = 0 6a + 17a2 + 12a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(6 + 17a + 12a2) = 0 Factor a trinomial. a((3 + 4a)(2 + 3a)) = 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 '(3 + 4a)' equal to zero and attempt to solve: Simplifying 3 + 4a = 0 Solving 3 + 4a = 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 + 4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a = 0 + -3 4a = 0 + -3 Combine like terms: 0 + -3 = -3 4a = -3 Divide each side by '4'. a = -0.75 Simplifying a = -0.75Subproblem 3
Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 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 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667Solution
a = {0, -0.75, -0.6666666667}
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