4n^2+144=48n

Solution for 4n^2+144=48n equation:

Simplifying
4n2 + 144 = 48n

Reorder the terms:
144 + 4n2 = 48n

Solving
144 + 4n2 = 48n

Solving for variable 'n'.

Reorder the terms:
144 + -48n + 4n2 = 48n + -48n

Combine like terms: 48n + -48n = 0
144 + -48n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + -12n + n2) = 0

Factor a trinomial.
4((6 + -1n)(6 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {6, 6}