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Simplifying (8 + -1v)(3v + 1) = 0 Reorder the terms: (8 + -1v)(1 + 3v) = 0 Multiply (8 + -1v) * (1 + 3v) (8(1 + 3v) + -1v * (1 + 3v)) = 0 ((1 * 8 + 3v * 8) + -1v * (1 + 3v)) = 0 ((8 + 24v) + -1v * (1 + 3v)) = 0 (8 + 24v + (1 * -1v + 3v * -1v)) = 0 (8 + 24v + (-1v + -3v2)) = 0 Combine like terms: 24v + -1v = 23v (8 + 23v + -3v2) = 0 Solving 8 + 23v + -3v2 = 0 Solving for variable 'v'. Factor a trinomial. (8 + -1v)(1 + 3v) = 0Subproblem 1
Set the factor '(8 + -1v)' equal to zero and attempt to solve: Simplifying 8 + -1v = 0 Solving 8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1v = 0 + -8 -1v = 0 + -8 Combine like terms: 0 + -8 = -8 -1v = -8 Divide each side by '-1'. v = 8 Simplifying v = 8Subproblem 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 = {8, -0.3333333333}
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