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Simplifying (3v + 7)(3 + v) = 0 Reorder the terms: (7 + 3v)(3 + v) = 0 Multiply (7 + 3v) * (3 + v) (7(3 + v) + 3v * (3 + v)) = 0 ((3 * 7 + v * 7) + 3v * (3 + v)) = 0 ((21 + 7v) + 3v * (3 + v)) = 0 (21 + 7v + (3 * 3v + v * 3v)) = 0 (21 + 7v + (9v + 3v2)) = 0 Combine like terms: 7v + 9v = 16v (21 + 16v + 3v2) = 0 Solving 21 + 16v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (3 + v)(7 + 3v) = 0Subproblem 1
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 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 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Subproblem 2
Set the factor '(7 + 3v)' equal to zero and attempt to solve: Simplifying 7 + 3v = 0 Solving 7 + 3v = 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 + 3v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3v = 0 + -7 3v = 0 + -7 Combine like terms: 0 + -7 = -7 3v = -7 Divide each side by '3'. v = -2.333333333 Simplifying v = -2.333333333Solution
v = {-3, -2.333333333}
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