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Simplifying (3 + -1v)(3v + 4) = 0 Reorder the terms: (3 + -1v)(4 + 3v) = 0 Multiply (3 + -1v) * (4 + 3v) (3(4 + 3v) + -1v * (4 + 3v)) = 0 ((4 * 3 + 3v * 3) + -1v * (4 + 3v)) = 0 ((12 + 9v) + -1v * (4 + 3v)) = 0 (12 + 9v + (4 * -1v + 3v * -1v)) = 0 (12 + 9v + (-4v + -3v2)) = 0 Combine like terms: 9v + -4v = 5v (12 + 5v + -3v2) = 0 Solving 12 + 5v + -3v2 = 0 Solving for variable 'v'. Factor a trinomial. (3 + -1v)(4 + 3v) = 0Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 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 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Subproblem 2
Set the factor '(4 + 3v)' equal to zero and attempt to solve: Simplifying 4 + 3v = 0 Solving 4 + 3v = 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 + 3v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3v = 0 + -4 3v = 0 + -4 Combine like terms: 0 + -4 = -4 3v = -4 Divide each side by '3'. v = -1.333333333 Simplifying v = -1.333333333Solution
v = {3, -1.333333333}
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