n^2(-7n^2+8n-6)=

Solution for n^2(-7n^2+8n-6)= equation:

Simplifying
n2(-7n2 + 8n + -6) = 0

Reorder the terms:
n2(-6 + 8n + -7n2) = 0
(-6 * n2 + 8n * n2 + -7n2 * n2) = 0
(-6n2 + 8n3 + -7n4) = 0

Solving
-6n2 + 8n3 + -7n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(-6 + 8n + -7n2) = 0

Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(-6 + 8n + -7n2)' equal to zero and attempt to solve:

Simplifying
-6 + 8n + -7n2 = 0

Solving
-6 + 8n + -7n2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.8571428571 + -1.142857143n + n2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -1.142857143n + -0.8571428571 + n2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -1.142857143n + n2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -1.142857143n + n2 = 0 + -0.8571428571
-1.142857143n + n2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-1.142857143n + n2 = -0.8571428571

The n term is -1.142857143n.  Take half its coefficient (-0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
-1.142857143n + 0.3265306123 + n2 = -0.8571428571 + 0.3265306123

Reorder the terms:
0.3265306123 + -1.142857143n + n2 = -0.8571428571 + 0.3265306123

Combine like terms: -0.8571428571 + 0.3265306123 = -0.5306122448
0.3265306123 + -1.142857143n + n2 = -0.5306122448

Factor a perfect square on the left side:
(n + -0.5714285715)(n + -0.5714285715) = -0.5306122448

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}