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Simplifying (3v + 7)(4 + v) = 0 Reorder the terms: (7 + 3v)(4 + v) = 0 Multiply (7 + 3v) * (4 + v) (7(4 + v) + 3v * (4 + v)) = 0 ((4 * 7 + v * 7) + 3v * (4 + v)) = 0 ((28 + 7v) + 3v * (4 + v)) = 0 (28 + 7v + (4 * 3v + v * 3v)) = 0 (28 + 7v + (12v + 3v2)) = 0 Combine like terms: 7v + 12v = 19v (28 + 19v + 3v2) = 0 Solving 28 + 19v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (4 + v)(7 + 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 '(7 + 3v)' equal to zero and attempt to solve: Simplifying 7 + 3v = 0 Solving 7 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3v = 0 + -7 3v = 0 + -7 Combine like terms: 0 + -7 = -7 3v = -7 Divide each side by '3'. v = -2.333333333 Simplifying v = -2.333333333Solution
v = {-4, -2.333333333}
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