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Simplifying (3 + v)(5 + v) = 0 Multiply (3 + v) * (5 + v) (3(5 + v) + v(5 + v)) = 0 ((5 * 3 + v * 3) + v(5 + v)) = 0 ((15 + 3v) + v(5 + v)) = 0 (15 + 3v + (5 * v + v * v)) = 0 (15 + 3v + (5v + v2)) = 0 Combine like terms: 3v + 5v = 8v (15 + 8v + v2) = 0 Solving 15 + 8v + v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + v)(3 + v) = 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 '(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 = -3Solution
v = {-5, -3}
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