2v^2+20v+52=4

Solution for 2v^2+20v+52=4 equation:

Simplifying
2v2 + 20v + 52 = 4

Reorder the terms:
52 + 20v + 2v2 = 4

Solving
52 + 20v + 2v2 = 4

Solving for variable 'v'.

Reorder the terms:
52 + -4 + 20v + 2v2 = 4 + -4

Combine like terms: 52 + -4 = 48
48 + 20v + 2v2 = 4 + -4

Combine like terms: 4 + -4 = 0
48 + 20v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 10v + v2) = 0

Factor a trinomial.
2((6 + v)(4 + v)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

Add '-4' to each side of the equation.
4 + -4 + v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v = 0 + -4
v = 0 + -4

Combine like terms: 0 + -4 = -4
v = -4

Simplifying
v = -4
Solution
v = {-6, -4}