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Simplifying 6v2 = 15 + 27v Solving 6v2 = 15 + 27v Solving for variable 'v'. Reorder the terms: -15 + -27v + 6v2 = 15 + 27v + -15 + -27v Reorder the terms: -15 + -27v + 6v2 = 15 + -15 + 27v + -27v Combine like terms: 15 + -15 = 0 -15 + -27v + 6v2 = 0 + 27v + -27v -15 + -27v + 6v2 = 27v + -27v Combine like terms: 27v + -27v = 0 -15 + -27v + 6v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -9v + 2v2) = 0 Factor a trinomial. 3((-1 + -2v)(5 + -1v)) = 0 Ignore the factor 3.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 '(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 = 5Solution
v = {-0.5, 5}
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