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Simplifying 12v2 + -118v + 210 = -4v Reorder the terms: 210 + -118v + 12v2 = -4v Solving 210 + -118v + 12v2 = -4v Solving for variable 'v'. Reorder the terms: 210 + -118v + 4v + 12v2 = -4v + 4v Combine like terms: -118v + 4v = -114v 210 + -114v + 12v2 = -4v + 4v Combine like terms: -4v + 4v = 0 210 + -114v + 12v2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(35 + -19v + 2v2) = 0 Factor a trinomial. 6((5 + -2v)(7 + -1v)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + -2v)' equal to zero and attempt to solve: Simplifying 5 + -2v = 0 Solving 5 + -2v = 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 + -2v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2v = 0 + -5 -2v = 0 + -5 Combine like terms: 0 + -5 = -5 -2v = -5 Divide each side by '-2'. v = 2.5 Simplifying v = 2.5Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7Solution
v = {2.5, 7}
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