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Simplifying (2v + 1)(8 + v) = 0 Reorder the terms: (1 + 2v)(8 + v) = 0 Multiply (1 + 2v) * (8 + v) (1(8 + v) + 2v * (8 + v)) = 0 ((8 * 1 + v * 1) + 2v * (8 + v)) = 0 ((8 + 1v) + 2v * (8 + v)) = 0 (8 + 1v + (8 * 2v + v * 2v)) = 0 (8 + 1v + (16v + 2v2)) = 0 Combine like terms: 1v + 16v = 17v (8 + 17v + 2v2) = 0 Solving 8 + 17v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (8 + v)(1 + 2v) = 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 '(1 + 2v)' equal to zero and attempt to solve: Simplifying 1 + 2v = 0 Solving 1 + 2v = 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 + 2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2v = 0 + -1 2v = 0 + -1 Combine like terms: 0 + -1 = -1 2v = -1 Divide each side by '2'. v = -0.5 Simplifying v = -0.5Solution
v = {-8, -0.5}
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