(4v+1)(9-v)=0

Solution for (4v+1)(9-v)=0 equation:

Simplifying
(4v + 1)(9 + -1v) = 0

Reorder the terms:
(1 + 4v)(9 + -1v) = 0

Multiply (1 + 4v) * (9 + -1v)
(1(9 + -1v) + 4v * (9 + -1v)) = 0
((9 * 1 + -1v * 1) + 4v * (9 + -1v)) = 0
((9 + -1v) + 4v * (9 + -1v)) = 0
(9 + -1v + (9 * 4v + -1v * 4v)) = 0
(9 + -1v + (36v + -4v2)) = 0

Combine like terms: -1v + 36v = 35v
(9 + 35v + -4v2) = 0

Solving
9 + 35v + -4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(9 + -1v)(1 + 4v) = 0

Subproblem 1
Set the factor '(9 + -1v)' equal to zero and attempt to solve:

Simplifying
9 + -1v = 0

Solving
9 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1v = 0 + -9
-1v = 0 + -9

Combine like terms: 0 + -9 = -9
-1v = -9

Divide each side by '-1'.
v = 9

Simplifying
v = 9
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 = {9, -0.25}