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Simplifying (4 + -1v)(4v + 3) = 0 Reorder the terms: (4 + -1v)(3 + 4v) = 0 Multiply (4 + -1v) * (3 + 4v) (4(3 + 4v) + -1v * (3 + 4v)) = 0 ((3 * 4 + 4v * 4) + -1v * (3 + 4v)) = 0 ((12 + 16v) + -1v * (3 + 4v)) = 0 (12 + 16v + (3 * -1v + 4v * -1v)) = 0 (12 + 16v + (-3v + -4v^{2})) = 0 Combine like terms: 16v + -3v = 13v (12 + 13v + -4v^{2}) = 0 Solving 12 + 13v + -4v^{2}= 0 Solving for variable 'v'. Factor a trinomial. (4 + -1v)(3 + 4v) = 0## Subproblem 1

Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4## Subproblem 2

Set the factor '(3 + 4v)' equal to zero and attempt to solve: Simplifying 3 + 4v = 0 Solving 3 + 4v = 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 + 4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4v = 0 + -3 4v = 0 + -3 Combine like terms: 0 + -3 = -3 4v = -3 Divide each side by '4'. v = -0.75 Simplifying v = -0.75## Solution

v = {4, -0.75}

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