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((7 + v)(6 + v)) = 0

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

Simplifying
7 + v = 0

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

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

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

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

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

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

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

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