1=2v^2+11v+6

Solution for 1=2v^2+11v+6 equation:

Simplifying
1 = 2v2 + 11v + 6

Reorder the terms:
1 = 6 + 11v + 2v2

Solving
1 = 6 + 11v + 2v2

Solving for variable 'v'.

Combine like terms: 1 + -6 = -5
-5 + -11v + -2v2 = 6 + 11v + 2v2 + -6 + -11v + -2v2

Reorder the terms:
-5 + -11v + -2v2 = 6 + -6 + 11v + -11v + 2v2 + -2v2

Combine like terms: 6 + -6 = 0
-5 + -11v + -2v2 = 0 + 11v + -11v + 2v2 + -2v2
-5 + -11v + -2v2 = 11v + -11v + 2v2 + -2v2

Combine like terms: 11v + -11v = 0
-5 + -11v + -2v2 = 0 + 2v2 + -2v2
-5 + -11v + -2v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-5 + -11v + -2v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 11v + 2v2) = 0

Factor a trinomial.
-1((5 + v)(1 + 2v)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 0

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

Add '-5' to each side of the equation.
5 + -5 + v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5
Subproblem 2
Set the factor '(1 + 2v)' equal to zero and attempt to solve:

Simplifying
1 + 2v = 0

Solving
1 + 2v = 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 + 2v = 0 + -1

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

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

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {-5, -0.5}