(3v+4)(7-v)=0

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Solution for (3v+4)(7-v)=0 equation: 


Simplifying
(3v + 4)(7 + -1v) = 0

Reorder the terms:
(4 + 3v)(7 + -1v) = 0

Multiply (4 + 3v) * (7 + -1v)
(4(7 + -1v) + 3v * (7 + -1v)) = 0
((7 * 4 + -1v * 4) + 3v * (7 + -1v)) = 0
((28 + -4v) + 3v * (7 + -1v)) = 0
(28 + -4v + (7 * 3v + -1v * 3v)) = 0
(28 + -4v + (21v + -3v2)) = 0

Combine like terms: -4v + 21v = 17v
(28 + 17v + -3v2) = 0

Solving
28 + 17v + -3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(7 + -1v)(4 + 3v) = 0


Subproblem 1
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 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 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7

Subproblem 2
Set the factor '(4 + 3v)' equal to zero and attempt to solve:

Simplifying
4 + 3v = 0

Solving
4 + 3v = 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 + 3v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3v = 0 + -4
3v = 0 + -4

Combine like terms: 0 + -4 = -4
3v = -4

Divide each side by '3'.
v = -1.333333333

Simplifying
v = -1.333333333
Solution
v = {7, -1.333333333}

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