n^2(-7n+5n-6)=0

Solution for n^2(-7n+5n-6)=0 equation:

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

Reorder the terms:
n2(-6 + -7n + 5n) = 0

Combine like terms: -7n + 5n = -2n
n2(-6 + -2n) = 0
(-6 * n2 + -2n * n2) = 0
(-6n2 + -2n3) = 0

Solving
-6n2 + -2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-2n2'.
-2n2(3 + n) = 0

Ignore the factor -2.
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 '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

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

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

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

Simplifying
n = -3
Solution
n = {0, -3}