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Simplifying 12a2v + -54av + -30v = 0 Reorder the terms: -54av + 12a2v + -30v = 0 Solving -54av + 12a2v + -30v = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6v'. 6v(-9a + 2a2 + -5) = 0 Factor a trinomial. 6v((a + -5)(2a + 1)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing a to the left, all other terms to the right. Add '-1v' to each side of the equation. v + -1v = 0 + -1v Remove the zero: 0 = -1v Simplifying 0 = -1v The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(a + -5)' equal to zero and attempt to solve: Simplifying a + -5 = 0 Reorder the terms: -5 + a = 0 Solving -5 + a = 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 + a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + a = 0 + 5 a = 0 + 5 Combine like terms: 0 + 5 = 5 a = 5 Simplifying a = 5Subproblem 3
Set the factor '(2a + 1)' equal to zero and attempt to solve: Simplifying 2a + 1 = 0 Reorder the terms: 1 + 2a = 0 Solving 1 + 2a = 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 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5Solution
a = {5, -0.5}
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