v^2+v+1=3

Solution for v^2+v+1=3 equation:

Simplifying
v2 + v + 1 = 3

Reorder the terms:
1 + v + v2 = 3

Solving
1 + v + v2 = 3

Solving for variable 'v'.

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

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

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

Factor a trinomial.
(-2 + -1v)(1 + -1v) = 0

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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

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

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

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

Simplifying
v = -2
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 = {-2, 1}