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Simplifying (2 + -1v)(4v + 9) = 0 Reorder the terms: (2 + -1v)(9 + 4v) = 0 Multiply (2 + -1v) * (9 + 4v) (2(9 + 4v) + -1v * (9 + 4v)) = 0 ((9 * 2 + 4v * 2) + -1v * (9 + 4v)) = 0 ((18 + 8v) + -1v * (9 + 4v)) = 0 (18 + 8v + (9 * -1v + 4v * -1v)) = 0 (18 + 8v + (-9v + -4v2)) = 0 Combine like terms: 8v + -9v = -1v (18 + -1v + -4v2) = 0 Solving 18 + -1v + -4v2 = 0 Solving for variable 'v'. Factor a trinomial. (2 + -1v)(9 + 4v) = 0Subproblem 1
Set the factor '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2Subproblem 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 = {2, -2.25}
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