36m^6+12m^4=m^2+0

Solution for 36m^6+12m^4=m^2+0 equation:

Simplifying
36m6 + 12m4 = m2 + 0

Reorder the terms:
12m4 + 36m6 = m2 + 0

Reorder the terms:
12m4 + 36m6 = 0 + m2
Remove the zero:
12m4 + 36m6 = m2

Solving
12m4 + 36m6 = m2

Solving for variable 'm'.

Reorder the terms:
-1m2 + 12m4 + 36m6 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-1m2 + 12m4 + 36m6 = 0

Factor out the Greatest Common Factor (GCF), 'm2'.
m2(-1 + 12m2 + 36m4) = 0

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 '(-1 + 12m2 + 36m4)' equal to zero and attempt to solve:

Simplifying
-1 + 12m2 + 36m4 = 0

Solving
-1 + 12m2 + 36m4 = 0

Begin completing the square.  Divide all terms by
36 the coefficient of the squared term: 

Divide each side by '36'.
-0.02777777778 + 0.3333333333m2 + m4 = 0

Move the constant term to the right:

Add '0.02777777778' to each side of the equation.
-0.02777777778 + 0.3333333333m2 + 0.02777777778 + m4 = 0 + 0.02777777778

Reorder the terms:
-0.02777777778 + 0.02777777778 + 0.3333333333m2 + m4 = 0 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + 0.3333333333m2 + m4 = 0 + 0.02777777778
0.3333333333m2 + m4 = 0 + 0.02777777778

Combine like terms: 0 + 0.02777777778 = 0.02777777778
0.3333333333m2 + m4 = 0.02777777778

The m term is 0.3333333333m2.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333m2 + 0.02777777779 + m4 = 0.02777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333m2 + m4 = 0.02777777778 + 0.02777777779

Combine like terms: 0.02777777778 + 0.02777777779 = 0.05555555557
0.02777777779 + 0.3333333333m2 + m4 = 0.05555555557

Factor a perfect square on the left side:
(m2 + 0.1666666667)(m2 + 0.1666666667) = 0.05555555557

Calculate the square root of the right side: 0.23570226

Break this problem into two subproblems by setting 
(m2 + 0.1666666667) equal to 0.23570226 and -0.23570226.

Subproblem 1
m2 + 0.1666666667 = 0.23570226

Simplifying
m2 + 0.1666666667 = 0.23570226

Reorder the terms:
0.1666666667 + m2 = 0.23570226

Solving
0.1666666667 + m2 = 0.23570226

Solving for variable 'm'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + m2 = 0.23570226 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + m2 = 0.23570226 + -0.1666666667
m2 = 0.23570226 + -0.1666666667

Combine like terms: 0.23570226 + -0.1666666667 = 0.0690355933
m2 = 0.0690355933

Simplifying
m2 = 0.0690355933

Take the square root of each side:
m = {-0.262746253, 0.262746253}

Subproblem 2
m2 + 0.1666666667 = -0.23570226

Simplifying
m2 + 0.1666666667 = -0.23570226

Reorder the terms:
0.1666666667 + m2 = -0.23570226

Solving
0.1666666667 + m2 = -0.23570226

Solving for variable 'm'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + m2 = -0.23570226 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + m2 = -0.23570226 + -0.1666666667
m2 = -0.23570226 + -0.1666666667

Combine like terms: -0.23570226 + -0.1666666667 = -0.4023689267
m2 = -0.4023689267

Simplifying
m2 = -0.4023689267

Reorder the terms:
0.4023689267 + m2 = -0.4023689267 + 0.4023689267

Combine like terms: -0.4023689267 + 0.4023689267 = 0.0000000000
0.4023689267 + m2 = 0.0000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
m = {0}