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Simplifying (4v + 2)(5 + v) = 0 Reorder the terms: (2 + 4v)(5 + v) = 0 Multiply (2 + 4v) * (5 + v) (2(5 + v) + 4v * (5 + v)) = 0 ((5 * 2 + v * 2) + 4v * (5 + v)) = 0 ((10 + 2v) + 4v * (5 + v)) = 0 (10 + 2v + (5 * 4v + v * 4v)) = 0 (10 + 2v + (20v + 4v2)) = 0 Combine like terms: 2v + 20v = 22v (10 + 22v + 4v2) = 0 Solving 10 + 22v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 11v + 2v2) = 0 Factor a trinomial. 2((5 + v)(1 + 2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve: Simplifying 5 + v = 0 Solving 5 + v = 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 + v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + v = 0 + -5 v = 0 + -5 Combine like terms: 0 + -5 = -5 v = -5 Simplifying v = -5Subproblem 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 = {-5, -0.5}
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