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Simplifying (2 + v)(4v + 5) = 0 Reorder the terms: (2 + v)(5 + 4v) = 0 Multiply (2 + v) * (5 + 4v) (2(5 + 4v) + v(5 + 4v)) = 0 ((5 * 2 + 4v * 2) + v(5 + 4v)) = 0 ((10 + 8v) + v(5 + 4v)) = 0 (10 + 8v + (5 * v + 4v * v)) = 0 (10 + 8v + (5v + 4v2)) = 0 Combine like terms: 8v + 5v = 13v (10 + 13v + 4v2) = 0 Solving 10 + 13v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (2 + v)(5 + 4v) = 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 + 4v)' equal to zero and attempt to solve: Simplifying 5 + 4v = 0 Solving 5 + 4v = 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 + 4v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4v = 0 + -5 4v = 0 + -5 Combine like terms: 0 + -5 = -5 4v = -5 Divide each side by '4'. v = -1.25 Simplifying v = -1.25Solution
v = {-2, -1.25}
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