21n^2-2n+1=4

Solution for 21n^2-2n+1=4 equation:

Simplifying
21n2 + -2n + 1 = 4

Reorder the terms:
1 + -2n + 21n2 = 4

Solving
1 + -2n + 21n2 = 4

Solving for variable 'n'.

Reorder the terms:
1 + -4 + -2n + 21n2 = 4 + -4

Combine like terms: 1 + -4 = -3
-3 + -2n + 21n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-3 + -2n + 21n2 = 0

Factor a trinomial.
(-1 + -3n)(3 + -7n) = 0

Subproblem 1
Set the factor '(-1 + -3n)' equal to zero and attempt to solve:

Simplifying
-1 + -3n = 0

Solving
-1 + -3n = 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 + -3n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3n = 0 + 1
-3n = 0 + 1

Combine like terms: 0 + 1 = 1
-3n = 1

Divide each side by '-3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Subproblem 2
Set the factor '(3 + -7n)' equal to zero and attempt to solve:

Simplifying
3 + -7n = 0

Solving
3 + -7n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7n = 0 + -3
-7n = 0 + -3

Combine like terms: 0 + -3 = -3
-7n = -3

Divide each side by '-7'.
n = 0.4285714286

Simplifying
n = 0.4285714286
Solution
n = {-0.3333333333, 0.4285714286}