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

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


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

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

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

Combine like terms: 7v + 3v = 10v
(7 + 10v + 3v2) = 0

Solving
7 + 10v + 3v2 = 0

Solving for variable 'v'.

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

Subproblem 1

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 = -2.333333333

Subproblem 2

Set the factor '(1 + v)' equal to zero and attempt to solve: Simplifying 1 + v = 0 Solving 1 + v = 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 + v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + v = 0 + -1 v = 0 + -1 Combine like terms: 0 + -1 = -1 v = -1 Simplifying v = -1

Solution

v = {-2.333333333, -1}

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