v^2+2v+1=2v^2+2v-1

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

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

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

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

Add '-2v' to each side of the equation.
1 + 2v + -2v + v2 = -1 + 2v + -2v + 2v2

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

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

Solving
1 + v2 = -1 + 2v2

Solving for variable 'v'.

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

Add '-2v2' to each side of the equation.
1 + v2 + -2v2 = -1 + 2v2 + -2v2

Combine like terms: v2 + -2v2 = -1v2
1 + -1v2 = -1 + 2v2 + -2v2

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

Add '-1' to each side of the equation.
1 + -1 + -1v2 = -1 + -1

Combine like terms: 1 + -1 = 0
0 + -1v2 = -1 + -1
-1v2 = -1 + -1

Combine like terms: -1 + -1 = -2
-1v2 = -2

Divide each side by '-1'.
v2 = 2

Simplifying
v2 = 2

Take the square root of each side:
v = {-1.414213562, 1.414213562}