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Simplifying 8v2 = 12 + 20v Solving 8v2 = 12 + 20v Solving for variable 'v'. Reorder the terms: -12 + -20v + 8v2 = 12 + 20v + -12 + -20v Reorder the terms: -12 + -20v + 8v2 = 12 + -12 + 20v + -20v Combine like terms: 12 + -12 = 0 -12 + -20v + 8v2 = 0 + 20v + -20v -12 + -20v + 8v2 = 20v + -20v Combine like terms: 20v + -20v = 0 -12 + -20v + 8v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -5v + 2v2) = 0 Factor a trinomial. 4((-1 + -2v)(3 + -1v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2v)' equal to zero and attempt to solve: Simplifying -1 + -2v = 0 Solving -1 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2v = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2v = 0 + 1 -2v = 0 + 1 Combine like terms: 0 + 1 = 1 -2v = 1 Divide each side by '-2'. v = -0.5 Simplifying v = -0.5Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 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 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {-0.5, 3}
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