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Simplifying (2v + 5)(2 + -1v) = 0 Reorder the terms: (5 + 2v)(2 + -1v) = 0 Multiply (5 + 2v) * (2 + -1v) (5(2 + -1v) + 2v * (2 + -1v)) = 0 ((2 * 5 + -1v * 5) + 2v * (2 + -1v)) = 0 ((10 + -5v) + 2v * (2 + -1v)) = 0 (10 + -5v + (2 * 2v + -1v * 2v)) = 0 (10 + -5v + (4v + -2v2)) = 0 Combine like terms: -5v + 4v = -1v (10 + -1v + -2v2) = 0 Solving 10 + -1v + -2v2 = 0 Solving for variable 'v'. Factor a trinomial. (2 + -1v)(5 + 2v) = 0Subproblem 1
Set the factor '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 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 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2Subproblem 2
Set the factor '(5 + 2v)' equal to zero and attempt to solve: Simplifying 5 + 2v = 0 Solving 5 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2v = 0 + -5 2v = 0 + -5 Combine like terms: 0 + -5 = -5 2v = -5 Divide each side by '2'. v = -2.5 Simplifying v = -2.5Solution
v = {2, -2.5}
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