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Simplifying (4v + 9)(3 + -1v) = 0 Reorder the terms: (9 + 4v)(3 + -1v) = 0 Multiply (9 + 4v) * (3 + -1v) (9(3 + -1v) + 4v * (3 + -1v)) = 0 ((3 * 9 + -1v * 9) + 4v * (3 + -1v)) = 0 ((27 + -9v) + 4v * (3 + -1v)) = 0 (27 + -9v + (3 * 4v + -1v * 4v)) = 0 (27 + -9v + (12v + -4v2)) = 0 Combine like terms: -9v + 12v = 3v (27 + 3v + -4v2) = 0 Solving 27 + 3v + -4v2 = 0 Solving for variable 'v'. Factor a trinomial. (3 + -1v)(9 + 4v) = 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 '(9 + 4v)' equal to zero and attempt to solve: Simplifying 9 + 4v = 0 Solving 9 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4v = 0 + -9 4v = 0 + -9 Combine like terms: 0 + -9 = -9 4v = -9 Divide each side by '4'. v = -2.25 Simplifying v = -2.25Solution
v = {3, -2.25}
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