5m^4+30m^3+25m^2=0

Solution for 5m^4+30m^3+25m^2=0 equation:

Simplifying
5m4 + 30m3 + 25m2 = 0

Reorder the terms:
25m2 + 30m3 + 5m4 = 0

Solving
25m2 + 30m3 + 5m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '5m2'.
5m2(5 + 6m + m2) = 0

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

Ignore the factor 5.
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 '(5 + m)' equal to zero and attempt to solve:

Simplifying
5 + m = 0

Solving
5 + m = 0

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

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

Combine like terms: 5 + -5 = 0
0 + m = 0 + -5
m = 0 + -5

Combine like terms: 0 + -5 = -5
m = -5

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

Simplifying
1 + m = 0

Solving
1 + m = 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 + m = 0 + -1

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

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

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