5n^2+18=-6+2n^2+27n

Solution for 5n^2+18=-6+2n^2+27n equation:

Simplifying
5n2 + 18 = -6 + 2n2 + 27n

Reorder the terms:
18 + 5n2 = -6 + 2n2 + 27n

Reorder the terms:
18 + 5n2 = -6 + 27n + 2n2

Solving
18 + 5n2 = -6 + 27n + 2n2

Solving for variable 'n'.

Reorder the terms:
18 + 6 + -27n + 5n2 + -2n2 = -6 + 27n + 2n2 + 6 + -27n + -2n2

Combine like terms: 18 + 6 = 24
24 + -27n + 5n2 + -2n2 = -6 + 27n + 2n2 + 6 + -27n + -2n2

Combine like terms: 5n2 + -2n2 = 3n2
24 + -27n + 3n2 = -6 + 27n + 2n2 + 6 + -27n + -2n2

Reorder the terms:
24 + -27n + 3n2 = -6 + 6 + 27n + -27n + 2n2 + -2n2

Combine like terms: -6 + 6 = 0
24 + -27n + 3n2 = 0 + 27n + -27n + 2n2 + -2n2
24 + -27n + 3n2 = 27n + -27n + 2n2 + -2n2

Combine like terms: 27n + -27n = 0
24 + -27n + 3n2 = 0 + 2n2 + -2n2
24 + -27n + 3n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
24 + -27n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -9n + n2) = 0

Factor a trinomial.
3((1 + -1n)(8 + -1n)) = 0

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

Simplifying
1 + -1n = 0

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

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

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

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

Simplifying
n = 1
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {1, 8}