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Simplifying 3v2 + 14v = -1v + -18 Reorder the terms: 14v + 3v2 = -1v + -18 Reorder the terms: 14v + 3v2 = -18 + -1v Solving 14v + 3v2 = -18 + -1v Solving for variable 'v'. Reorder the terms: 18 + 14v + v + 3v2 = -18 + -1v + 18 + v Combine like terms: 14v + v = 15v 18 + 15v + 3v2 = -18 + -1v + 18 + v Reorder the terms: 18 + 15v + 3v2 = -18 + 18 + -1v + v Combine like terms: -18 + 18 = 0 18 + 15v + 3v2 = 0 + -1v + v 18 + 15v + 3v2 = -1v + v Combine like terms: -1v + v = 0 18 + 15v + 3v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 5v + v2) = 0 Factor a trinomial. 3((3 + v)(2 + v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 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 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Subproblem 2
Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2Solution
v = {-3, -2}
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