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Simplifying (2v + 7)(5 + -1v) = 0 Reorder the terms: (7 + 2v)(5 + -1v) = 0 Multiply (7 + 2v) * (5 + -1v) (7(5 + -1v) + 2v * (5 + -1v)) = 0 ((5 * 7 + -1v * 7) + 2v * (5 + -1v)) = 0 ((35 + -7v) + 2v * (5 + -1v)) = 0 (35 + -7v + (5 * 2v + -1v * 2v)) = 0 (35 + -7v + (10v + -2v2)) = 0 Combine like terms: -7v + 10v = 3v (35 + 3v + -2v2) = 0 Solving 35 + 3v + -2v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + -1v)(7 + 2v) = 0Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 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 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Subproblem 2
Set the factor '(7 + 2v)' equal to zero and attempt to solve: Simplifying 7 + 2v = 0 Solving 7 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2v = 0 + -7 2v = 0 + -7 Combine like terms: 0 + -7 = -7 2v = -7 Divide each side by '2'. v = -3.5 Simplifying v = -3.5Solution
v = {5, -3.5}
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