(v-21)(6v+1)=0

Solution for (v-21)(6v+1)=0 equation:

Simplifying
(v + -21)(6v + 1) = 0

Reorder the terms:
(-21 + v)(6v + 1) = 0

Reorder the terms:
(-21 + v)(1 + 6v) = 0

Multiply (-21 + v) * (1 + 6v)
(-21(1 + 6v) + v(1 + 6v)) = 0
((1 * -21 + 6v * -21) + v(1 + 6v)) = 0
((-21 + -126v) + v(1 + 6v)) = 0
(-21 + -126v + (1 * v + 6v * v)) = 0
(-21 + -126v + (1v + 6v2)) = 0

Combine like terms: -126v + 1v = -125v
(-21 + -125v + 6v2) = 0

Solving
-21 + -125v + 6v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-1 + -6v)(21 + -1v) = 0

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

Simplifying
-1 + -6v = 0

Solving
-1 + -6v = 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 + -6v = 0 + 1

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

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

Divide each side by '-6'.
v = -0.1666666667

Simplifying
v = -0.1666666667
Subproblem 2
Set the factor '(21 + -1v)' equal to zero and attempt to solve:

Simplifying
21 + -1v = 0

Solving
21 + -1v = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1v = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1v = 0 + -21
-1v = 0 + -21

Combine like terms: 0 + -21 = -21
-1v = -21

Divide each side by '-1'.
v = 21

Simplifying
v = 21
Solution
v = {-0.1666666667, 21}