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Simplifying (2v + 3)(7 + v) = 0 Reorder the terms: (3 + 2v)(7 + v) = 0 Multiply (3 + 2v) * (7 + v) (3(7 + v) + 2v * (7 + v)) = 0 ((7 * 3 + v * 3) + 2v * (7 + v)) = 0 ((21 + 3v) + 2v * (7 + v)) = 0 (21 + 3v + (7 * 2v + v * 2v)) = 0 (21 + 3v + (14v + 2v2)) = 0 Combine like terms: 3v + 14v = 17v (21 + 17v + 2v2) = 0 Solving 21 + 17v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (7 + v)(3 + 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 '(3 + 2v)' equal to zero and attempt to solve: Simplifying 3 + 2v = 0 Solving 3 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2v = 0 + -3 2v = 0 + -3 Combine like terms: 0 + -3 = -3 2v = -3 Divide each side by '2'. v = -1.5 Simplifying v = -1.5Solution
v = {-7, -1.5}
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