3n^2=-18n+21

Solution for 3n^2=-18n+21 equation:

Simplifying
3n2 = -18n + 21

Reorder the terms:
3n2 = 21 + -18n

Solving
3n2 = 21 + -18n

Solving for variable 'n'.

Reorder the terms:
-21 + 18n + 3n2 = 21 + -18n + -21 + 18n

Reorder the terms:
-21 + 18n + 3n2 = 21 + -21 + -18n + 18n

Combine like terms: 21 + -21 = 0
-21 + 18n + 3n2 = 0 + -18n + 18n
-21 + 18n + 3n2 = -18n + 18n

Combine like terms: -18n + 18n = 0
-21 + 18n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 6n + n2) = 0

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

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

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
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
Solution
n = {-7, 1}