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Simplifying (3v + -5)(3 + v) = 0 Reorder the terms: (-5 + 3v)(3 + v) = 0 Multiply (-5 + 3v) * (3 + v) (-5(3 + v) + 3v * (3 + v)) = 0 ((3 * -5 + v * -5) + 3v * (3 + v)) = 0 ((-15 + -5v) + 3v * (3 + v)) = 0 (-15 + -5v + (3 * 3v + v * 3v)) = 0 (-15 + -5v + (9v + 3v2)) = 0 Combine like terms: -5v + 9v = 4v (-15 + 4v + 3v2) = 0 Solving -15 + 4v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(5 + -3v) = 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 '(5 + -3v)' equal to zero and attempt to solve: Simplifying 5 + -3v = 0 Solving 5 + -3v = 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 + -3v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3v = 0 + -5 -3v = 0 + -5 Combine like terms: 0 + -5 = -5 -3v = -5 Divide each side by '-3'. v = 1.666666667 Simplifying v = 1.666666667Solution
v = {-3, 1.666666667}
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