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Simplifying (3v + 1)(5v + -1) = 0 Reorder the terms: (1 + 3v)(5v + -1) = 0 Reorder the terms: (1 + 3v)(-1 + 5v) = 0 Multiply (1 + 3v) * (-1 + 5v) (1(-1 + 5v) + 3v * (-1 + 5v)) = 0 ((-1 * 1 + 5v * 1) + 3v * (-1 + 5v)) = 0 ((-1 + 5v) + 3v * (-1 + 5v)) = 0 (-1 + 5v + (-1 * 3v + 5v * 3v)) = 0 (-1 + 5v + (-3v + 15v2)) = 0 Combine like terms: 5v + -3v = 2v (-1 + 2v + 15v2) = 0 Solving -1 + 2v + 15v2 = 0 Solving for variable 'v'. Factor a trinomial. (-1 + -3v)(1 + -5v) = 0Subproblem 1
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 = -0.3333333333Subproblem 2
Set the factor '(1 + -5v)' equal to zero and attempt to solve: Simplifying 1 + -5v = 0 Solving 1 + -5v = 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 + -5v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5v = 0 + -1 -5v = 0 + -1 Combine like terms: 0 + -1 = -1 -5v = -1 Divide each side by '-5'. v = 0.2 Simplifying v = 0.2Solution
v = {-0.3333333333, 0.2}
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