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Simplifying -6v2 + 27v = 12 Reorder the terms: 27v + -6v2 = 12 Solving 27v + -6v2 = 12 Solving for variable 'v'. Reorder the terms: -12 + 27v + -6v2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 27v + -6v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 9v + -2v2) = 0 Factor a trinomial. 3((-4 + v)(1 + -2v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + v)' equal to zero and attempt to solve: Simplifying -4 + v = 0 Solving -4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = 0 + 4 Combine like terms: -4 + 4 = 0 0 + v = 0 + 4 v = 0 + 4 Combine like terms: 0 + 4 = 4 v = 4 Simplifying v = 4Subproblem 2
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 = 0.5Solution
v = {4, 0.5}
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