21n^2=-54+81n

Solution for 21n^2=-54+81n equation:

Simplifying
21n2 = -54 + 81n

Solving
21n2 = -54 + 81n

Solving for variable 'n'.

Reorder the terms:
54 + -81n + 21n2 = -54 + 81n + 54 + -81n

Reorder the terms:
54 + -81n + 21n2 = -54 + 54 + 81n + -81n

Combine like terms: -54 + 54 = 0
54 + -81n + 21n2 = 0 + 81n + -81n
54 + -81n + 21n2 = 81n + -81n

Combine like terms: 81n + -81n = 0
54 + -81n + 21n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -27n + 7n2) = 0

Factor a trinomial.
3((6 + -7n)(3 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

Solving
6 + -7n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7n = 0 + -6
-7n = 0 + -6

Combine like terms: 0 + -6 = -6
-7n = -6

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0.8571428571, 3}