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Simplifying (3v + 4)(9 + v) = 0 Reorder the terms: (4 + 3v)(9 + v) = 0 Multiply (4 + 3v) * (9 + v) (4(9 + v) + 3v * (9 + v)) = 0 ((9 * 4 + v * 4) + 3v * (9 + v)) = 0 ((36 + 4v) + 3v * (9 + v)) = 0 (36 + 4v + (9 * 3v + v * 3v)) = 0 (36 + 4v + (27v + 3v2)) = 0 Combine like terms: 4v + 27v = 31v (36 + 31v + 3v2) = 0 Solving 36 + 31v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (9 + v)(4 + 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 '(4 + 3v)' equal to zero and attempt to solve: Simplifying 4 + 3v = 0 Solving 4 + 3v = 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 + 3v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3v = 0 + -4 3v = 0 + -4 Combine like terms: 0 + -4 = -4 3v = -4 Divide each side by '3'. v = -1.333333333 Simplifying v = -1.333333333Solution
v = {-9, -1.333333333}
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