(4v-1)(6+v)=0

Solution for (4v-1)(6+v)=0 equation:

Simplifying
(4v + -1)(6 + v) = 0

Reorder the terms:
(-1 + 4v)(6 + v) = 0

Multiply (-1 + 4v) * (6 + v)
(-1(6 + v) + 4v * (6 + v)) = 0
((6 * -1 + v * -1) + 4v * (6 + v)) = 0
((-6 + -1v) + 4v * (6 + v)) = 0
(-6 + -1v + (6 * 4v + v * 4v)) = 0
(-6 + -1v + (24v + 4v2)) = 0

Combine like terms: -1v + 24v = 23v
(-6 + 23v + 4v2) = 0

Solving
-6 + 23v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-6 + -1v)(1 + -4v) = 0

Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6
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 = {-6, 0.25}