v^2+6v=27

Solution for v^2+6v=27 equation:

Simplifying
v2 + 6v = 27

Reorder the terms:
6v + v2 = 27

Solving
6v + v2 = 27

Solving for variable 'v'.

Reorder the terms:
-27 + 6v + v2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 6v + v2 = 0

Factor a trinomial.
(-9 + -1v)(3 + -1v) = 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 '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {-9, 3}