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Simplifying (3v + 2)(5 + v) = 0 Reorder the terms: (2 + 3v)(5 + v) = 0 Multiply (2 + 3v) * (5 + v) (2(5 + v) + 3v * (5 + v)) = 0 ((5 * 2 + v * 2) + 3v * (5 + v)) = 0 ((10 + 2v) + 3v * (5 + v)) = 0 (10 + 2v + (5 * 3v + v * 3v)) = 0 (10 + 2v + (15v + 3v2)) = 0 Combine like terms: 2v + 15v = 17v (10 + 17v + 3v2) = 0 Solving 10 + 17v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + v)(2 + 3v) = 0Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve: Simplifying 5 + v = 0 Solving 5 + v = 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 + v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + v = 0 + -5 v = 0 + -5 Combine like terms: 0 + -5 = -5 v = -5 Simplifying v = -5Subproblem 2
Set the factor '(2 + 3v)' equal to zero and attempt to solve: Simplifying 2 + 3v = 0 Solving 2 + 3v = 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 + 3v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3v = 0 + -2 3v = 0 + -2 Combine like terms: 0 + -2 = -2 3v = -2 Divide each side by '3'. v = -0.6666666667 Simplifying v = -0.6666666667Solution
v = {-5, -0.6666666667}
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