(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((-7 + -2v)(1 + -1v)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
v = {-3.5, 1}