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Simplifying (3v + 1)(9 + v) = 0 Reorder the terms: (1 + 3v)(9 + v) = 0 Multiply (1 + 3v) * (9 + v) (1(9 + v) + 3v * (9 + v)) = 0 ((9 * 1 + v * 1) + 3v * (9 + v)) = 0 ((9 + 1v) + 3v * (9 + v)) = 0 (9 + 1v + (9 * 3v + v * 3v)) = 0 (9 + 1v + (27v + 3v2)) = 0 Combine like terms: 1v + 27v = 28v (9 + 28v + 3v2) = 0 Solving 9 + 28v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (9 + v)(1 + 3v) = 0Subproblem 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 + 3v)' equal to zero and attempt to solve: Simplifying 1 + 3v = 0 Solving 1 + 3v = 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 + 3v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3v = 0 + -1 3v = 0 + -1 Combine like terms: 0 + -1 = -1 3v = -1 Divide each side by '3'. v = -0.3333333333 Simplifying v = -0.3333333333Solution
v = {-9, -0.3333333333}
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