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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 = 1v (-24 + 1v + 3v2) = 0 Solving -24 + 1v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(8 + -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 '(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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