(5v+1)(8-v)=0

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Solution for (5v+1)(8-v)=0 equation: 


Simplifying
(5v + 1)(8 + -1v) = 0

Reorder the terms:
(1 + 5v)(8 + -1v) = 0

Multiply (1 + 5v) * (8 + -1v)
(1(8 + -1v) + 5v * (8 + -1v)) = 0
((8 * 1 + -1v * 1) + 5v * (8 + -1v)) = 0
((8 + -1v) + 5v * (8 + -1v)) = 0
(8 + -1v + (8 * 5v + -1v * 5v)) = 0
(8 + -1v + (40v + -5v2)) = 0

Combine like terms: -1v + 40v = 39v
(8 + 39v + -5v2) = 0

Solving
8 + 39v + -5v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(8 + -1v)(1 + 5v) = 0


Subproblem 1
Set the factor '(8 + -1v)' equal to zero and attempt to solve:

Simplifying
8 + -1v = 0

Solving
8 + -1v = 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 + -1v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1v = 0 + -8
-1v = 0 + -8

Combine like terms: 0 + -8 = -8
-1v = -8

Divide each side by '-1'.
v = 8

Simplifying
v = 8

Subproblem 2
Set the factor '(1 + 5v)' equal to zero and attempt to solve:

Simplifying
1 + 5v = 0

Solving
1 + 5v = 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 + 5v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5v = 0 + -1
5v = 0 + -1

Combine like terms: 0 + -1 = -1
5v = -1

Divide each side by '5'.
v = -0.2

Simplifying
v = -0.2
Solution
v = {8, -0.2}

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