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Simplifying (5v + 1)(5 + v) = 0 Reorder the terms: (1 + 5v)(5 + v) = 0 Multiply (1 + 5v) * (5 + v) (1(5 + v) + 5v * (5 + v)) = 0 ((5 * 1 + v * 1) + 5v * (5 + v)) = 0 ((5 + 1v) + 5v * (5 + v)) = 0 (5 + 1v + (5 * 5v + v * 5v)) = 0 (5 + 1v + (25v + 5v2)) = 0 Combine like terms: 1v + 25v = 26v (5 + 26v + 5v2) = 0 Solving 5 + 26v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + v)(1 + 5v) = 0Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve: Simplifying 5 + v = 0 Solving 5 + v = 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 + v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + v = 0 + -5 v = 0 + -5 Combine like terms: 0 + -5 = -5 v = -5 Simplifying v = -5Subproblem 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 = {-5, -0.2}
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