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Simplifying (8 + -1v)(4v + 5) = 0 Reorder the terms: (8 + -1v)(5 + 4v) = 0 Multiply (8 + -1v) * (5 + 4v) (8(5 + 4v) + -1v * (5 + 4v)) = 0 ((5 * 8 + 4v * 8) + -1v * (5 + 4v)) = 0 ((40 + 32v) + -1v * (5 + 4v)) = 0 (40 + 32v + (5 * -1v + 4v * -1v)) = 0 (40 + 32v + (-5v + -4v2)) = 0 Combine like terms: 32v + -5v = 27v (40 + 27v + -4v2) = 0 Solving 40 + 27v + -4v2 = 0 Solving for variable 'v'. Factor a trinomial. (8 + -1v)(5 + 4v) = 0Subproblem 1
Set the factor '(8 + -1v)' equal to zero and attempt to solve: Simplifying 8 + -1v = 0 Solving 8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1v = 0 + -8 -1v = 0 + -8 Combine like terms: 0 + -8 = -8 -1v = -8 Divide each side by '-1'. v = 8 Simplifying v = 8Subproblem 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 = {8, -1.25}
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