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Simplifying 6a3 + 7a2 = 3a Reorder the terms: 7a2 + 6a3 = 3a Solving 7a2 + 6a3 = 3a Solving for variable 'a'. Reorder the terms: -3a + 7a2 + 6a3 = 3a + -3a Combine like terms: 3a + -3a = 0 -3a + 7a2 + 6a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-3 + 7a + 6a2) = 0 Factor a trinomial. a((-3 + -2a)(1 + -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 + -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 '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 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 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Solution
a = {0, -1.5, 0.3333333333}
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