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Simplifying (2v + 9)(5 + v) = 0 Reorder the terms: (9 + 2v)(5 + v) = 0 Multiply (9 + 2v) * (5 + v) (9(5 + v) + 2v * (5 + v)) = 0 ((5 * 9 + v * 9) + 2v * (5 + v)) = 0 ((45 + 9v) + 2v * (5 + v)) = 0 (45 + 9v + (5 * 2v + v * 2v)) = 0 (45 + 9v + (10v + 2v2)) = 0 Combine like terms: 9v + 10v = 19v (45 + 19v + 2v2) = 0 Solving 45 + 19v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + v)(9 + 2v) = 0Subproblem 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 '(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 = -4.5Solution
v = {-5, -4.5}
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