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Simplifying (4v + 5)(6 + v) = 0 Reorder the terms: (5 + 4v)(6 + v) = 0 Multiply (5 + 4v) * (6 + v) (5(6 + v) + 4v * (6 + v)) = 0 ((6 * 5 + v * 5) + 4v * (6 + v)) = 0 ((30 + 5v) + 4v * (6 + v)) = 0 (30 + 5v + (6 * 4v + v * 4v)) = 0 (30 + 5v + (24v + 4v2)) = 0 Combine like terms: 5v + 24v = 29v (30 + 29v + 4v2) = 0 Solving 30 + 29v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (6 + v)(5 + 4v) = 0Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6Subproblem 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 = {-6, -1.25}
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