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Simplifying (4v + -9)(2 + v) = 0 Reorder the terms: (-9 + 4v)(2 + v) = 0 Multiply (-9 + 4v) * (2 + v) (-9(2 + v) + 4v * (2 + v)) = 0 ((2 * -9 + v * -9) + 4v * (2 + v)) = 0 ((-18 + -9v) + 4v * (2 + v)) = 0 (-18 + -9v + (2 * 4v + v * 4v)) = 0 (-18 + -9v + (8v + 4v2)) = 0 Combine like terms: -9v + 8v = -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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