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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 = 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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