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Simplifying (2v + -5)(9 + v) = 0 Reorder the terms: (-5 + 2v)(9 + v) = 0 Multiply (-5 + 2v) * (9 + v) (-5(9 + v) + 2v * (9 + v)) = 0 ((9 * -5 + v * -5) + 2v * (9 + v)) = 0 ((-45 + -5v) + 2v * (9 + v)) = 0 (-45 + -5v + (9 * 2v + v * 2v)) = 0 (-45 + -5v + (18v + 2v2)) = 0 Combine like terms: -5v + 18v = 13v (-45 + 13v + 2v2) = 0 Solving -45 + 13v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (-9 + -1v)(5 + -2v) = 0Subproblem 1
Set the factor '(-9 + -1v)' equal to zero and attempt to solve: Simplifying -9 + -1v = 0 Solving -9 + -1v = 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 + -1v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1v = 0 + 9 -1v = 0 + 9 Combine like terms: 0 + 9 = 9 -1v = 9 Divide each side by '-1'. v = -9 Simplifying v = -9Subproblem 2
Set the factor '(5 + -2v)' equal to zero and attempt to solve: Simplifying 5 + -2v = 0 Solving 5 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2v = 0 + -5 -2v = 0 + -5 Combine like terms: 0 + -5 = -5 -2v = -5 Divide each side by '-2'. v = 2.5 Simplifying v = 2.5Solution
v = {-9, 2.5}
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