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Simplifying (3 + -1v)(2v + 9) = 0 Reorder the terms: (3 + -1v)(9 + 2v) = 0 Multiply (3 + -1v) * (9 + 2v) (3(9 + 2v) + -1v * (9 + 2v)) = 0 ((9 * 3 + 2v * 3) + -1v * (9 + 2v)) = 0 ((27 + 6v) + -1v * (9 + 2v)) = 0 (27 + 6v + (9 * -1v + 2v * -1v)) = 0 (27 + 6v + (-9v + -2v2)) = 0 Combine like terms: 6v + -9v = -3v (27 + -3v + -2v2) = 0 Solving 27 + -3v + -2v2 = 0 Solving for variable 'v'. Factor a trinomial. (3 + -1v)(9 + 2v) = 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 + 2v)' equal to zero and attempt to solve: Simplifying 9 + 2v = 0 Solving 9 + 2v = 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 + 2v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2v = 0 + -9 2v = 0 + -9 Combine like terms: 0 + -9 = -9 2v = -9 Divide each side by '2'. v = -4.5 Simplifying v = -4.5Solution
v = {3, -4.5}
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