5v^2+v+1=7

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

Simplifying
5v2 + v + 1 = 7

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

Solving
1 + v + 5v2 = 7

Solving for variable 'v'.

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

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

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

Factor a trinomial.
(-6 + -5v)(1 + -1v) = 0

Subproblem 1
Set the factor '(-6 + -5v)' equal to zero and attempt to solve:

Simplifying
-6 + -5v = 0

Solving
-6 + -5v = 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 + -5v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5v = 0 + 6
-5v = 0 + 6

Combine like terms: 0 + 6 = 6
-5v = 6

Divide each side by '-5'.
v = -1.2

Simplifying
v = -1.2
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 = {-1.2, 1}