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Simplifying 12a3 + -1a2 = 35a Reorder the terms: -1a2 + 12a3 = 35a Solving -1a2 + 12a3 = 35a Solving for variable 'a'. Reorder the terms: -35a + -1a2 + 12a3 = 35a + -35a Combine like terms: 35a + -35a = 0 -35a + -1a2 + 12a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-35 + -1a + 12a2) = 0 Factor a trinomial. a((-5 + -3a)(7 + -4a)) = 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 + -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 3
Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 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 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75Solution
a = {0, -1.666666667, 1.75}
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