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Simplifying (3v + 1)(9 + -1v) = 0 Reorder the terms: (1 + 3v)(9 + -1v) = 0 Multiply (1 + 3v) * (9 + -1v) (1(9 + -1v) + 3v * (9 + -1v)) = 0 ((9 * 1 + -1v * 1) + 3v * (9 + -1v)) = 0 ((9 + -1v) + 3v * (9 + -1v)) = 0 (9 + -1v + (9 * 3v + -1v * 3v)) = 0 (9 + -1v + (27v + -3v2)) = 0 Combine like terms: -1v + 27v = 26v (9 + 26v + -3v2) = 0 Solving 9 + 26v + -3v2 = 0 Solving for variable 'v'. Factor a trinomial. (9 + -1v)(1 + 3v) = 0Subproblem 1
Set the factor '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 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 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. 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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