(3v+1)(7+v)=0

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Solution for (3v+1)(7+v)=0 equation:


Simplifying
(3v + 1)(7 + v) = 0

Reorder the terms:
(1 + 3v)(7 + v) = 0

Multiply (1 + 3v) * (7 + v)
(1(7 + v) + 3v * (7 + v)) = 0
((7 * 1 + v * 1) + 3v * (7 + v)) = 0
((7 + 1v) + 3v * (7 + v)) = 0
(7 + 1v + (7 * 3v + v * 3v)) = 0
(7 + 1v + (21v + 3v2)) = 0

Combine like terms: 1v + 21v = 22v
(7 + 22v + 3v2) = 0

Solving
7 + 22v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(7 + v)(1 + 3v) = 0

Subproblem 1

Set the factor '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 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 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7

Subproblem 2

Set the factor '(1 + 3v)' equal to zero and attempt to solve: Simplifying 1 + 3v = 0 Solving 1 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3v = 0 + -1 3v = 0 + -1 Combine like terms: 0 + -1 = -1 3v = -1 Divide each side by '3'. v = -0.3333333333 Simplifying v = -0.3333333333

Solution

v = {-7, -0.3333333333}

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