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Simplifying 36v3 + 42v2 + -540v = 0 Reorder the terms: -540v + 42v2 + 36v3 = 0 Solving -540v + 42v2 + 36v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6v'. 6v(-90 + 7v + 6v2) = 0 Factor a trinomial. 6v((-9 + -2v)(10 + -3v)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(-9 + -2v)' equal to zero and attempt to solve: Simplifying -9 + -2v = 0 Solving -9 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2v = 0 + 9 -2v = 0 + 9 Combine like terms: 0 + 9 = 9 -2v = 9 Divide each side by '-2'. v = -4.5 Simplifying v = -4.5Subproblem 3
Set the factor '(10 + -3v)' equal to zero and attempt to solve: Simplifying 10 + -3v = 0 Solving 10 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3v = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3v = 0 + -10 -3v = 0 + -10 Combine like terms: 0 + -10 = -10 -3v = -10 Divide each side by '-3'. v = 3.333333333 Simplifying v = 3.333333333Solution
v = {0, -4.5, 3.333333333}
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