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Simplifying 15v + 60 + 9v = 4v2 + 16v Reorder the terms: 60 + 15v + 9v = 4v2 + 16v Combine like terms: 15v + 9v = 24v 60 + 24v = 4v2 + 16v Reorder the terms: 60 + 24v = 16v + 4v2 Solving 60 + 24v = 16v + 4v2 Solving for variable 'v'. Combine like terms: 24v + -16v = 8v 60 + 8v + -4v2 = 16v + 4v2 + -16v + -4v2 Reorder the terms: 60 + 8v + -4v2 = 16v + -16v + 4v2 + -4v2 Combine like terms: 16v + -16v = 0 60 + 8v + -4v2 = 0 + 4v2 + -4v2 60 + 8v + -4v2 = 4v2 + -4v2 Combine like terms: 4v2 + -4v2 = 0 60 + 8v + -4v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(15 + 2v + -1v2) = 0 Factor a trinomial. 4((5 + -1v)(3 + v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 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 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Solution
v = {5, -3}
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