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Simplifying (2v + 5)(7 + v) = 0 Reorder the terms: (5 + 2v)(7 + v) = 0 Multiply (5 + 2v) * (7 + v) (5(7 + v) + 2v * (7 + v)) = 0 ((7 * 5 + v * 5) + 2v * (7 + v)) = 0 ((35 + 5v) + 2v * (7 + v)) = 0 (35 + 5v + (7 * 2v + v * 2v)) = 0 (35 + 5v + (14v + 2v2)) = 0 Combine like terms: 5v + 14v = 19v (35 + 19v + 2v2) = 0 Solving 35 + 19v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (7 + v)(5 + 2v) = 0Subproblem 1
Set the factor '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 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 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7Subproblem 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 = {-7, -2.5}
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