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Simplifying (9 + v)(3v + -1) = 0 Reorder the terms: (9 + v)(-1 + 3v) = 0 Multiply (9 + v) * (-1 + 3v) (9(-1 + 3v) + v(-1 + 3v)) = 0 ((-1 * 9 + 3v * 9) + v(-1 + 3v)) = 0 ((-9 + 27v) + v(-1 + 3v)) = 0 (-9 + 27v + (-1 * v + 3v * v)) = 0 (-9 + 27v + (-1v + 3v2)) = 0 Combine like terms: 27v + -1v = 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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