4n^2+9=12n

Solution for 4n^2+9=12n equation:

Simplifying
4n2 + 9 = 12n

Reorder the terms:
9 + 4n2 = 12n

Solving
9 + 4n2 = 12n

Solving for variable 'n'.

Reorder the terms:
9 + -12n + 4n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
9 + -12n + 4n2 = 0

Factor a trinomial.
(3 + -2n)(3 + -2n) = 0

Subproblem 1
Set the factor '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {1.5, 1.5}