3+n^2-4n-12=4n

Solution for 3+n^2-4n-12=4n equation:

Simplifying
3 + n2 + -4n + -12 = 4n

Reorder the terms:
3 + -12 + -4n + n2 = 4n

Combine like terms: 3 + -12 = -9
-9 + -4n + n2 = 4n

Solving
-9 + -4n + n2 = 4n

Solving for variable 'n'.

Reorder the terms:
-9 + -4n + -4n + n2 = 4n + -4n

Combine like terms: -4n + -4n = -8n
-9 + -8n + n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
-9 + -8n + n2 = 0

Factor a trinomial.
(-1 + -1n)(9 + -1n) = 0

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 '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-1, 9}