4n(3n^2+n-4)-n(3-n)=

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

Simplifying
4n(3n2 + n + -4) + -1n(3 + -1n) = 0

Reorder the terms:
4n(-4 + n + 3n2) + -1n(3 + -1n) = 0
(-4 * 4n + n * 4n + 3n2 * 4n) + -1n(3 + -1n) = 0
(-16n + 4n2 + 12n3) + -1n(3 + -1n) = 0
-16n + 4n2 + 12n3 + (3 * -1n + -1n * -1n) = 0
-16n + 4n2 + 12n3 + (-3n + 1n2) = 0

Reorder the terms:
-16n + -3n + 4n2 + 1n2 + 12n3 = 0

Combine like terms: -16n + -3n = -19n
-19n + 4n2 + 1n2 + 12n3 = 0

Combine like terms: 4n2 + 1n2 = 5n2
-19n + 5n2 + 12n3 = 0

Solving
-19n + 5n2 + 12n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-19 + 5n + 12n2) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-19 + 5n + 12n2)' equal to zero and attempt to solve:

Simplifying
-19 + 5n + 12n2 = 0

Solving
-19 + 5n + 12n2 = 0

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
-1.583333333 + 0.4166666667n + n2 = 0

Move the constant term to the right:

Add '1.583333333' to each side of the equation.
-1.583333333 + 0.4166666667n + 1.583333333 + n2 = 0 + 1.583333333

Reorder the terms:
-1.583333333 + 1.583333333 + 0.4166666667n + n2 = 0 + 1.583333333

Combine like terms: -1.583333333 + 1.583333333 = 0.000000000
0.000000000 + 0.4166666667n + n2 = 0 + 1.583333333
0.4166666667n + n2 = 0 + 1.583333333

Combine like terms: 0 + 1.583333333 = 1.583333333
0.4166666667n + n2 = 1.583333333

The n term is 0.4166666667n.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667n + 0.04340277781 + n2 = 1.583333333 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667n + n2 = 1.583333333 + 0.04340277781

Combine like terms: 1.583333333 + 0.04340277781 = 1.62673611081
0.04340277781 + 0.4166666667n + n2 = 1.62673611081

Factor a perfect square on the left side:
(n + 0.2083333334)(n + 0.2083333334) = 1.62673611081

Calculate the square root of the right side: 1.275435655

Break this problem into two subproblems by setting 
(n + 0.2083333334) equal to 1.275435655 and -1.275435655.

Subproblem 1
n + 0.2083333334 = 1.275435655

Simplifying
n + 0.2083333334 = 1.275435655

Reorder the terms:
0.2083333334 + n = 1.275435655

Solving
0.2083333334 + n = 1.275435655

Solving for variable 'n'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + n = 1.275435655 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + n = 1.275435655 + -0.2083333334
n = 1.275435655 + -0.2083333334

Combine like terms: 1.275435655 + -0.2083333334 = 1.0671023216
n = 1.0671023216

Simplifying
n = 1.0671023216

Subproblem 2
n + 0.2083333334 = -1.275435655

Simplifying
n + 0.2083333334 = -1.275435655

Reorder the terms:
0.2083333334 + n = -1.275435655

Solving
0.2083333334 + n = -1.275435655

Solving for variable 'n'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + n = -1.275435655 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + n = -1.275435655 + -0.2083333334
n = -1.275435655 + -0.2083333334

Combine like terms: -1.275435655 + -0.2083333334 = -1.4837689884
n = -1.4837689884

Simplifying
n = -1.4837689884

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.0671023216, -1.4837689884}
Solution
n = {0, 1.0671023216, -1.4837689884}