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

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

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

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

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

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

Combine like terms: 6v + -21v = -15v
(-21 + -15v + 6v2) = 0

Solving
-21 + -15v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -5v + 2v2) = 0

Factor a trinomial.
3((-1 + -1v)(7 + -2v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1v)' equal to zero and attempt to solve:

Simplifying
-1 + -1v = 0

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

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

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

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

Simplifying
v = -1
Subproblem 2
Set the factor '(7 + -2v)' equal to zero and attempt to solve:

Simplifying
7 + -2v = 0

Solving
7 + -2v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2v = 0 + -7
-2v = 0 + -7

Combine like terms: 0 + -7 = -7
-2v = -7

Divide each side by '-2'.
v = 3.5

Simplifying
v = 3.5
Solution
v = {-1, 3.5}