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Simplifying -12v = 4v2 + 9 Reorder the terms: -12v = 9 + 4v2 Solving -12v = 9 + 4v2 Solving for variable 'v'. Reorder the terms: -9 + -12v + -4v2 = 9 + 4v2 + -9 + -4v2 Reorder the terms: -9 + -12v + -4v2 = 9 + -9 + 4v2 + -4v2 Combine like terms: 9 + -9 = 0 -9 + -12v + -4v2 = 0 + 4v2 + -4v2 -9 + -12v + -4v2 = 4v2 + -4v2 Combine like terms: 4v2 + -4v2 = 0 -9 + -12v + -4v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 12v + 4v2) = 0 Factor a trinomial. -1((3 + 2v)(3 + 2v)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2v)' equal to zero and attempt to solve: Simplifying 3 + 2v = 0 Solving 3 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2v = 0 + -3 2v = 0 + -3 Combine like terms: 0 + -3 = -3 2v = -3 Divide each side by '2'. v = -1.5 Simplifying v = -1.5Subproblem 2
Set the factor '(3 + 2v)' equal to zero and attempt to solve: Simplifying 3 + 2v = 0 Solving 3 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2v = 0 + -3 2v = 0 + -3 Combine like terms: 0 + -3 = -3 2v = -3 Divide each side by '2'. v = -1.5 Simplifying v = -1.5Solution
v = {-1.5, -1.5}
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