3m^2(m^2-4mn-5n^2)=

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Solution for 3m^2(m^2-4mn-5n^2)= equation: 


Simplifying
3m2(m2 + -4mn + -5n2) = 0

Reorder the terms:
3m2(-4mn + m2 + -5n2) = 0
(-4mn * 3m2 + m2 * 3m2 + -5n2 * 3m2) = 0

Reorder the terms:
(-15m2n2 + -12m3n + 3m4) = 0
(-15m2n2 + -12m3n + 3m4) = 0

Solving
-15m2n2 + -12m3n + 3m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3m2'.
3m2(-5n2 + -4mn + m2) = 0

Factor a trinomial.
3m2((-1n + -1m)(5n + -1m)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve:

Simplifying
m2 = 0

Solving
m2 = 0

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

Simplifying
m2 = 0

Take the square root of each side:
m = {0}

Subproblem 2
Set the factor '(-1n + -1m)' equal to zero and attempt to solve:

Simplifying
-1n + -1m = 0

Reorder the terms:
-1m + -1n = 0

Solving
-1m + -1n = 0

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

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

Combine like terms: -1n + n = 0
-1m + 0 = 0 + n
-1m = 0 + n
Remove the zero:
-1m = n

Divide each side by '-1'.
m = -1n

Simplifying
m = -1n

Subproblem 3
Set the factor '(5n + -1m)' equal to zero and attempt to solve:

Simplifying
5n + -1m = 0

Reorder the terms:
-1m + 5n = 0

Solving
-1m + 5n = 0

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

Add '-5n' to each side of the equation.
-1m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
-1m + 0 = 0 + -5n
-1m = 0 + -5n
Remove the zero:
-1m = -5n

Divide each side by '-1'.
m = 5n

Simplifying
m = 5n
Solution
m = {0, -1n, 5n}

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