(3m+n^2)(3m+n^2)=

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Solution for (3m+n^2)(3m+n^2)= equation: 


Simplifying
(3m + n2)(3m + n2) = 0

Multiply (3m + n2) * (3m + n2)
(3m * (3m + n2) + n2(3m + n2)) = 0
((3m * 3m + n2 * 3m) + n2(3m + n2)) = 0

Reorder the terms:
((3mn2 + 9m2) + n2(3m + n2)) = 0
((3mn2 + 9m2) + n2(3m + n2)) = 0
(3mn2 + 9m2 + (3m * n2 + n2 * n2)) = 0
(3mn2 + 9m2 + (3mn2 + n4)) = 0

Reorder the terms:
(3mn2 + 3mn2 + 9m2 + n4) = 0

Combine like terms: 3mn2 + 3mn2 = 6mn2
(6mn2 + 9m2 + n4) = 0

Solving
6mn2 + 9m2 + n4 = 0

Solving for variable 'm'.

Factor a trinomial.
(3m + n2)(3m + n2) = 0


Subproblem 1
Set the factor '(3m + n2)' equal to zero and attempt to solve:

Simplifying
3m + n2 = 0

Solving
3m + n2 = 0

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

Add '-1n2' to each side of the equation.
3m + n2 + -1n2 = 0 + -1n2

Combine like terms: n2 + -1n2 = 0
3m + 0 = 0 + -1n2
3m = 0 + -1n2
Remove the zero:
3m = -1n2

Divide each side by '3'.
m = -0.3333333333n2

Simplifying
m = -0.3333333333n2

Subproblem 2
Set the factor '(3m + n2)' equal to zero and attempt to solve:

Simplifying
3m + n2 = 0

Solving
3m + n2 = 0

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

Add '-1n2' to each side of the equation.
3m + n2 + -1n2 = 0 + -1n2

Combine like terms: n2 + -1n2 = 0
3m + 0 = 0 + -1n2
3m = 0 + -1n2
Remove the zero:
3m = -1n2

Divide each side by '3'.
m = -0.3333333333n2

Simplifying
m = -0.3333333333n2
Solution
m = {-0.3333333333n2, -0.3333333333n2}

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