v(v-6)=27

Solution for v(v-6)=27 equation:

Simplifying
v(v + -6) = 27

Reorder the terms:
v(-6 + v) = 27
(-6 * v + v * v) = 27
(-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.
(-3 + -1v)(9 + -1v) = 0

Subproblem 1
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
Subproblem 2
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
Solution
v = {-3, 9}