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Simplifying (3v + 5)(2 + v) = 0 Reorder the terms: (5 + 3v)(2 + v) = 0 Multiply (5 + 3v) * (2 + v) (5(2 + v) + 3v * (2 + v)) = 0 ((2 * 5 + v * 5) + 3v * (2 + v)) = 0 ((10 + 5v) + 3v * (2 + v)) = 0 (10 + 5v + (2 * 3v + v * 3v)) = 0 (10 + 5v + (6v + 3v2)) = 0 Combine like terms: 5v + 6v = 11v (10 + 11v + 3v2) = 0 Solving 10 + 11v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (2 + v)(5 + 3v) = 0Subproblem 1
Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2Subproblem 2
Set the factor '(5 + 3v)' equal to zero and attempt to solve: Simplifying 5 + 3v = 0 Solving 5 + 3v = 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 + 3v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3v = 0 + -5 3v = 0 + -5 Combine like terms: 0 + -5 = -5 3v = -5 Divide each side by '3'. v = -1.666666667 Simplifying v = -1.666666667Solution
v = {-2, -1.666666667}
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