(4v-1)(8-v)=0

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Solution for (4v-1)(8-v)=0 equation: 


Simplifying
(4v + -1)(8 + -1v) = 0

Reorder the terms:
(-1 + 4v)(8 + -1v) = 0

Multiply (-1 + 4v) * (8 + -1v)
(-1(8 + -1v) + 4v * (8 + -1v)) = 0
((8 * -1 + -1v * -1) + 4v * (8 + -1v)) = 0
((-8 + 1v) + 4v * (8 + -1v)) = 0
(-8 + 1v + (8 * 4v + -1v * 4v)) = 0
(-8 + 1v + (32v + -4v2)) = 0

Combine like terms: 1v + 32v = 33v
(-8 + 33v + -4v2) = 0

Solving
-8 + 33v + -4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-8 + v)(1 + -4v) = 0


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

Simplifying
-8 + v = 0

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

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

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

Simplifying
v = 8

Subproblem 2
Set the factor '(1 + -4v)' equal to zero and attempt to solve:

Simplifying
1 + -4v = 0

Solving
1 + -4v = 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 + -4v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4v = 0 + -1
-4v = 0 + -1

Combine like terms: 0 + -1 = -1
-4v = -1

Divide each side by '-4'.
v = 0.25

Simplifying
v = 0.25
Solution
v = {8, 0.25}

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