20n^2+21n+1=0

Solution for 20n^2+21n+1=0 equation:

Simplifying
20n2 + 21n + 1 = 0

Reorder the terms:
1 + 21n + 20n2 = 0

Solving
1 + 21n + 20n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + n)(1 + 20n) = 0

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Subproblem 2
Set the factor '(1 + 20n)' equal to zero and attempt to solve:

Simplifying
1 + 20n = 0

Solving
1 + 20n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 20n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 20n = 0 + -1
20n = 0 + -1

Combine like terms: 0 + -1 = -1
20n = -1

Divide each side by '20'.
n = -0.05

Simplifying
n = -0.05
Solution
n = {-1, -0.05}