6v^2-78v+252=0

Solution for 6v^2-78v+252=0 equation:

Simplifying
6v2 + -78v + 252 = 0

Reorder the terms:
252 + -78v + 6v2 = 0

Solving
252 + -78v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6'.
6(42 + -13v + v2) = 0

Factor a trinomial.
6((6 + -1v)(7 + -1v)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 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 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {6, 7}