v^2+2v+1=2v^2+7v-5

Solution for v^2+2v+1=2v^2+7v-5 equation:

Simplifying
v2 + 2v + 1 = 2v2 + 7v + -5

Reorder the terms:
1 + 2v + v2 = 2v2 + 7v + -5

Reorder the terms:
1 + 2v + v2 = -5 + 7v + 2v2

Solving
1 + 2v + v2 = -5 + 7v + 2v2

Solving for variable 'v'.

Reorder the terms:
1 + 5 + 2v + -7v + v2 + -2v2 = -5 + 7v + 2v2 + 5 + -7v + -2v2

Combine like terms: 1 + 5 = 6
6 + 2v + -7v + v2 + -2v2 = -5 + 7v + 2v2 + 5 + -7v + -2v2

Combine like terms: 2v + -7v = -5v
6 + -5v + v2 + -2v2 = -5 + 7v + 2v2 + 5 + -7v + -2v2

Combine like terms: v2 + -2v2 = -1v2
6 + -5v + -1v2 = -5 + 7v + 2v2 + 5 + -7v + -2v2

Reorder the terms:
6 + -5v + -1v2 = -5 + 5 + 7v + -7v + 2v2 + -2v2

Combine like terms: -5 + 5 = 0
6 + -5v + -1v2 = 0 + 7v + -7v + 2v2 + -2v2
6 + -5v + -1v2 = 7v + -7v + 2v2 + -2v2

Combine like terms: 7v + -7v = 0
6 + -5v + -1v2 = 0 + 2v2 + -2v2
6 + -5v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
6 + -5v + -1v2 = 0

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

Subproblem 1
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
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 = {1, -6}