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Simplifying (3v + 8)(4 + v) = 0 Reorder the terms: (8 + 3v)(4 + v) = 0 Multiply (8 + 3v) * (4 + v) (8(4 + v) + 3v * (4 + v)) = 0 ((4 * 8 + v * 8) + 3v * (4 + v)) = 0 ((32 + 8v) + 3v * (4 + v)) = 0 (32 + 8v + (4 * 3v + v * 3v)) = 0 (32 + 8v + (12v + 3v2)) = 0 Combine like terms: 8v + 12v = 20v (32 + 20v + 3v2) = 0 Solving 32 + 20v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (4 + v)(8 + 3v) = 0Subproblem 1
Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4Subproblem 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 = {-4, -2.666666667}
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