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

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

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

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

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