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Simplifying 30v2 + 123v + 120 = 0 Reorder the terms: 120 + 123v + 30v2 = 0 Solving 120 + 123v + 30v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(40 + 41v + 10v2) = 0 Factor a trinomial. 3((5 + 2v)(8 + 5v)) = 0 Ignore the factor 3.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 '(8 + 5v)' equal to zero and attempt to solve: Simplifying 8 + 5v = 0 Solving 8 + 5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5v = 0 + -8 5v = 0 + -8 Combine like terms: 0 + -8 = -8 5v = -8 Divide each side by '5'. v = -1.6 Simplifying v = -1.6Solution
v = {-2.5, -1.6}
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