v^2+6v=72

Solution for v^2+6v=72 equation:

Simplifying
v2 + 6v = 72

Reorder the terms:
6v + v2 = 72

Solving
6v + v2 = 72

Solving for variable 'v'.

Reorder the terms:
-72 + 6v + v2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 6v + v2 = 0

Factor a trinomial.
(-12 + -1v)(6 + -1v) = 0

Subproblem 1
Set the factor '(-12 + -1v)' equal to zero and attempt to solve:

Simplifying
-12 + -1v = 0

Solving
-12 + -1v = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1v = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1v = 0 + 12
-1v = 0 + 12

Combine like terms: 0 + 12 = 12
-1v = 12

Divide each side by '-1'.
v = -12

Simplifying
v = -12
Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

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

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

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {-12, 6}