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Simplifying (2v + 9)(3 + v) = 0 Reorder the terms: (9 + 2v)(3 + v) = 0 Multiply (9 + 2v) * (3 + v) (9(3 + v) + 2v * (3 + v)) = 0 ((3 * 9 + v * 9) + 2v * (3 + v)) = 0 ((27 + 9v) + 2v * (3 + v)) = 0 (27 + 9v + (3 * 2v + v * 2v)) = 0 (27 + 9v + (6v + 2v2)) = 0 Combine like terms: 9v + 6v = 15v (27 + 15v + 2v2) = 0 Solving 27 + 15v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (9 + 2v)(3 + 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 '(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 = -3Solution
v = {-4.5, -3}
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