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Simplifying (2v + 9)(4 + v) = 0 Reorder the terms: (9 + 2v)(4 + v) = 0 Multiply (9 + 2v) * (4 + v) (9(4 + v) + 2v * (4 + v)) = 0 ((4 * 9 + v * 9) + 2v * (4 + v)) = 0 ((36 + 9v) + 2v * (4 + v)) = 0 (36 + 9v + (4 * 2v + v * 2v)) = 0 (36 + 9v + (8v + 2v2)) = 0 Combine like terms: 9v + 8v = 17v (36 + 17v + 2v2) = 0 Solving 36 + 17v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (9 + 2v)(4 + v) = 0Subproblem 1
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 2
Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4Solution
v = {-4.5, -4}
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