5v^2+4v=1

Solution for 5v^2+4v=1 equation:

Simplifying
5v2 + 4v = 1

Reorder the terms:
4v + 5v2 = 1

Solving
4v + 5v2 = 1

Solving for variable 'v'.

Reorder the terms:
-1 + 4v + 5v2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4v + 5v2 = 0

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

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

Simplifying
1 + -5v = 0

Solving
1 + -5v = 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 + -5v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5v = 0 + -1
-5v = 0 + -1

Combine like terms: 0 + -1 = -1
-5v = -1

Divide each side by '-5'.
v = 0.2

Simplifying
v = 0.2
Solution
v = {-1, 0.2}