4v^2=12v+72

Solution for 4v^2=12v+72 equation:

Simplifying
4v2 = 12v + 72

Reorder the terms:
4v2 = 72 + 12v

Solving
4v2 = 72 + 12v

Solving for variable 'v'.

Reorder the terms:
-72 + -12v + 4v2 = 72 + 12v + -72 + -12v

Reorder the terms:
-72 + -12v + 4v2 = 72 + -72 + 12v + -12v

Combine like terms: 72 + -72 = 0
-72 + -12v + 4v2 = 0 + 12v + -12v
-72 + -12v + 4v2 = 12v + -12v

Combine like terms: 12v + -12v = 0
-72 + -12v + 4v2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -3v + v2) = 0

Factor a trinomial.
4((-3 + -1v)(6 + -1v)) = 0

Ignore the factor 4.
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 '(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 = {-3, 6}