2v^2+6v+1=v^2+4v+4

Solution for 2v^2+6v+1=v^2+4v+4 equation:

Simplifying
2v2 + 6v + 1 = v2 + 4v + 4

Reorder the terms:
1 + 6v + 2v2 = v2 + 4v + 4

Reorder the terms:
1 + 6v + 2v2 = 4 + 4v + v2

Solving
1 + 6v + 2v2 = 4 + 4v + v2

Solving for variable 'v'.

Reorder the terms:
1 + -4 + 6v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 1 + -4 = -3
-3 + 6v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 6v + -4v = 2v
-3 + 2v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-3 + 2v + 1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Reorder the terms:
-3 + 2v + 1v2 = 4 + -4 + 4v + -4v + v2 + -1v2

Combine like terms: 4 + -4 = 0
-3 + 2v + 1v2 = 0 + 4v + -4v + v2 + -1v2
-3 + 2v + 1v2 = 4v + -4v + v2 + -1v2

Combine like terms: 4v + -4v = 0
-3 + 2v + 1v2 = 0 + v2 + -1v2
-3 + 2v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-3 + 2v + 1v2 = 0

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

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 '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1
Solution
v = {-3, 1}