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Simplifying (3 + v)(2v + -9) = 0 Reorder the terms: (3 + v)(-9 + 2v) = 0 Multiply (3 + v) * (-9 + 2v) (3(-9 + 2v) + v(-9 + 2v)) = 0 ((-9 * 3 + 2v * 3) + v(-9 + 2v)) = 0 ((-27 + 6v) + v(-9 + 2v)) = 0 (-27 + 6v + (-9 * v + 2v * v)) = 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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