6n^2(n-5)-2n(4n^2+n-7)=

Solution for 6n^2(n-5)-2n(4n^2+n-7)= equation:

Simplifying
6n2(n + -5) + -2n(4n2 + n + -7) = 0

Reorder the terms:
6n2(-5 + n) + -2n(4n2 + n + -7) = 0
(-5 * 6n2 + n * 6n2) + -2n(4n2 + n + -7) = 0
(-30n2 + 6n3) + -2n(4n2 + n + -7) = 0

Reorder the terms:
-30n2 + 6n3 + -2n(-7 + n + 4n2) = 0
-30n2 + 6n3 + (-7 * -2n + n * -2n + 4n2 * -2n) = 0
-30n2 + 6n3 + (14n + -2n2 + -8n3) = 0

Reorder the terms:
14n + -30n2 + -2n2 + 6n3 + -8n3 = 0

Combine like terms: -30n2 + -2n2 = -32n2
14n + -32n2 + 6n3 + -8n3 = 0

Combine like terms: 6n3 + -8n3 = -2n3
14n + -32n2 + -2n3 = 0

Solving
14n + -32n2 + -2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(7 + -16n + -1n2) = 0

Ignore the factor 2.
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 '(7 + -16n + -1n2)' equal to zero and attempt to solve:

Simplifying
7 + -16n + -1n2 = 0

Solving
7 + -16n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + 16n + n2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 16n + 7 + n2 = 0 + 7

Reorder the terms:
-7 + 7 + 16n + n2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 16n + n2 = 0 + 7
16n + n2 = 0 + 7

Combine like terms: 0 + 7 = 7
16n + n2 = 7

The n term is 16n.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16n + 64 + n2 = 7 + 64

Reorder the terms:
64 + 16n + n2 = 7 + 64

Combine like terms: 7 + 64 = 71
64 + 16n + n2 = 71

Factor a perfect square on the left side:
(n + 8)(n + 8) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(n + 8) equal to 8.426149773 and -8.426149773.

Subproblem 1
n + 8 = 8.426149773

Simplifying
n + 8 = 8.426149773

Reorder the terms:
8 + n = 8.426149773

Solving
8 + n = 8.426149773

Solving for variable 'n'.

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

Add '-8' to each side of the equation.
8 + -8 + n = 8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + n = 8.426149773 + -8
n = 8.426149773 + -8

Combine like terms: 8.426149773 + -8 = 0.426149773
n = 0.426149773

Simplifying
n = 0.426149773

Subproblem 2
n + 8 = -8.426149773

Simplifying
n + 8 = -8.426149773

Reorder the terms:
8 + n = -8.426149773

Solving
8 + n = -8.426149773

Solving for variable 'n'.

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

Add '-8' to each side of the equation.
8 + -8 + n = -8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + n = -8.426149773 + -8
n = -8.426149773 + -8

Combine like terms: -8.426149773 + -8 = -16.426149773
n = -16.426149773

Simplifying
n = -16.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.426149773, -16.426149773}
Solution
n = {0, 0.426149773, -16.426149773}