12M^2N+24M^3N^2-36M^4N^3=0

Solution for 12M^2N+24M^3N^2-36M^4N^3=0 equation:

Simplifying
12M2N + 24M3N2 + -36M4N3 = 0

Solving
12M2N + 24M3N2 + -36M4N3 = 0

Solving for variable 'M'.

Factor out the Greatest Common Factor (GCF), '12M2N'.
12M2N(1 + 2MN + -3M2N2) = 0

Factor a trinomial.
12M2N((1 + -1MN)(1 + 3MN)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor 'M2N' equal to zero and attempt to solve:

Simplifying
M2N = 0

Solving
M2N = 0

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

Simplifying
M2N = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -1MN)' equal to zero and attempt to solve:

Simplifying
1 + -1MN = 0

Solving
1 + -1MN = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1MN = 0 + -1
-1MN = 0 + -1

Combine like terms: 0 + -1 = -1
-1MN = -1

Divide each side by '-1N'.
M = N-1

Simplifying
M = N-1
Subproblem 3
Set the factor '(1 + 3MN)' equal to zero and attempt to solve:

Simplifying
1 + 3MN = 0

Solving
1 + 3MN = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3MN = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3MN = 0 + -1
3MN = 0 + -1

Combine like terms: 0 + -1 = -1
3MN = -1

Divide each side by '3N'.
M = -0.3333333333N-1

Simplifying
M = -0.3333333333N-1
Solution
M = {N-1, -0.3333333333N-1}