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Simplifying (3v + 8)(3 + v) = 0 Reorder the terms: (8 + 3v)(3 + v) = 0 Multiply (8 + 3v) * (3 + v) (8(3 + v) + 3v * (3 + v)) = 0 ((3 * 8 + v * 8) + 3v * (3 + v)) = 0 ((24 + 8v) + 3v * (3 + v)) = 0 (24 + 8v + (3 * 3v + v * 3v)) = 0 (24 + 8v + (9v + 3v2)) = 0 Combine like terms: 8v + 9v = 17v (24 + 17v + 3v2) = 0 Solving 24 + 17v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (3 + v)(8 + 3v) = 0Subproblem 1
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 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 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Subproblem 2
Set the factor '(8 + 3v)' equal to zero and attempt to solve: Simplifying 8 + 3v = 0 Solving 8 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3v = 0 + -8 3v = 0 + -8 Combine like terms: 0 + -8 = -8 3v = -8 Divide each side by '3'. v = -2.666666667 Simplifying v = -2.666666667Solution
v = {-3, -2.666666667}
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