4n^2-3n-16n+12=0

Solution for 4n^2-3n-16n+12=0 equation:

Simplifying
4n2 + -3n + -16n + 12 = 0

Reorder the terms:
12 + -3n + -16n + 4n2 = 0

Combine like terms: -3n + -16n = -19n
12 + -19n + 4n2 = 0

Solving
12 + -19n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + -4n)(4 + -1n) = 0

Subproblem 1
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {0.75, 4}