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Simplifying (3v + 2)(8 + v) = 0 Reorder the terms: (2 + 3v)(8 + v) = 0 Multiply (2 + 3v) * (8 + v) (2(8 + v) + 3v * (8 + v)) = 0 ((8 * 2 + v * 2) + 3v * (8 + v)) = 0 ((16 + 2v) + 3v * (8 + v)) = 0 (16 + 2v + (8 * 3v + v * 3v)) = 0 (16 + 2v + (24v + 3v2)) = 0 Combine like terms: 2v + 24v = 26v (16 + 26v + 3v2) = 0 Solving 16 + 26v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (8 + v)(2 + 3v) = 0Subproblem 1
Set the factor '(8 + v)' equal to zero and attempt to solve: Simplifying 8 + v = 0 Solving 8 + v = 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 + v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + v = 0 + -8 v = 0 + -8 Combine like terms: 0 + -8 = -8 v = -8 Simplifying v = -8Subproblem 2
Set the factor '(2 + 3v)' equal to zero and attempt to solve: Simplifying 2 + 3v = 0 Solving 2 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3v = 0 + -2 3v = 0 + -2 Combine like terms: 0 + -2 = -2 3v = -2 Divide each side by '3'. v = -0.6666666667 Simplifying v = -0.6666666667Solution
v = {-8, -0.6666666667}
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