3n^2=6n+9

Solution for 3n^2=6n+9 equation:

Simplifying
3n2 = 6n + 9

Reorder the terms:
3n2 = 9 + 6n

Solving
3n2 = 9 + 6n

Solving for variable 'n'.

Reorder the terms:
-9 + -6n + 3n2 = 9 + 6n + -9 + -6n

Reorder the terms:
-9 + -6n + 3n2 = 9 + -9 + 6n + -6n

Combine like terms: 9 + -9 = 0
-9 + -6n + 3n2 = 0 + 6n + -6n
-9 + -6n + 3n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-9 + -6n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -2n + n2) = 0

Factor a trinomial.
3((-1 + -1n)(3 + -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 '(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 = {-1, 3}