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Simplifying (3v + -1)(6 + -1v) = 0 Reorder the terms: (-1 + 3v)(6 + -1v) = 0 Multiply (-1 + 3v) * (6 + -1v) (-1(6 + -1v) + 3v * (6 + -1v)) = 0 ((6 * -1 + -1v * -1) + 3v * (6 + -1v)) = 0 ((-6 + 1v) + 3v * (6 + -1v)) = 0 (-6 + 1v + (6 * 3v + -1v * 3v)) = 0 (-6 + 1v + (18v + -3v2)) = 0 Combine like terms: 1v + 18v = 19v (-6 + 19v + -3v2) = 0 Solving -6 + 19v + -3v2 = 0 Solving for variable 'v'. Factor a trinomial. (-6 + v)(1 + -3v) = 0Subproblem 1
Set the factor '(-6 + v)' equal to zero and attempt to solve: Simplifying -6 + v = 0 Solving -6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = 0 + 6 Combine like terms: -6 + 6 = 0 0 + v = 0 + 6 v = 0 + 6 Combine like terms: 0 + 6 = 6 v = 6 Simplifying v = 6Subproblem 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 = {6, 0.3333333333}
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