3v^2+6v+1=10

Solution for 3v^2+6v+1=10 equation:

Simplifying
3v2 + 6v + 1 = 10

Reorder the terms:
1 + 6v + 3v2 = 10

Solving
1 + 6v + 3v2 = 10

Solving for variable 'v'.

Reorder the terms:
1 + -10 + 6v + 3v2 = 10 + -10

Combine like terms: 1 + -10 = -9
-9 + 6v + 3v2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9 + 6v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 2v + v2) = 0

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

Ignore the factor 3.
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}