21n^2-13n+4=2

Solution for 21n^2-13n+4=2 equation:

Simplifying
21n2 + -13n + 4 = 2

Reorder the terms:
4 + -13n + 21n2 = 2

Solving
4 + -13n + 21n2 = 2

Solving for variable 'n'.

Reorder the terms:
4 + -2 + -13n + 21n2 = 2 + -2

Combine like terms: 4 + -2 = 2
2 + -13n + 21n2 = 2 + -2

Combine like terms: 2 + -2 = 0
2 + -13n + 21n2 = 0

Factor a trinomial.
(2 + -7n)(1 + -3n) = 0

Subproblem 1
Set the factor '(2 + -7n)' equal to zero and attempt to solve:

Simplifying
2 + -7n = 0

Solving
2 + -7n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7n = 0 + -2
-7n = 0 + -2

Combine like terms: 0 + -2 = -2
-7n = -2

Divide each side by '-7'.
n = 0.2857142857

Simplifying
n = 0.2857142857
Subproblem 2
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
Solution
n = {0.2857142857, 0.3333333333}