(3v+8)(7-v)=0

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Solution for (3v+8)(7-v)=0 equation: 


Simplifying
(3v + 8)(7 + -1v) = 0

Reorder the terms:
(8 + 3v)(7 + -1v) = 0

Multiply (8 + 3v) * (7 + -1v)
(8(7 + -1v) + 3v * (7 + -1v)) = 0
((7 * 8 + -1v * 8) + 3v * (7 + -1v)) = 0
((56 + -8v) + 3v * (7 + -1v)) = 0
(56 + -8v + (7 * 3v + -1v * 3v)) = 0
(56 + -8v + (21v + -3v2)) = 0

Combine like terms: -8v + 21v = 13v
(56 + 13v + -3v2) = 0

Solving
56 + 13v + -3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(7 + -1v)(8 + 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 '(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 = -2.666666667
Solution
v = {7, -2.666666667}

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