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Simplifying (4v + 2)(9 + v) = 0 Reorder the terms: (2 + 4v)(9 + v) = 0 Multiply (2 + 4v) * (9 + v) (2(9 + v) + 4v * (9 + v)) = 0 ((9 * 2 + v * 2) + 4v * (9 + v)) = 0 ((18 + 2v) + 4v * (9 + v)) = 0 (18 + 2v + (9 * 4v + v * 4v)) = 0 (18 + 2v + (36v + 4v2)) = 0 Combine like terms: 2v + 36v = 38v (18 + 38v + 4v2) = 0 Solving 18 + 38v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 19v + 2v2) = 0 Factor a trinomial. 2((9 + v)(1 + 2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + v)' equal to zero and attempt to solve: Simplifying 9 + v = 0 Solving 9 + v = 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 + v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + v = 0 + -9 v = 0 + -9 Combine like terms: 0 + -9 = -9 v = -9 Simplifying v = -9Subproblem 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 = {-9, -0.5}
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