4m^2x^2-24mx^2+36x^2-4(x^2+mx^2)(9)=0

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Solution for 4m^2x^2-24mx^2+36x^2-4(x^2+mx^2)(9)=0 equation: 


Simplifying
4m2x2 + -24mx2 + 36x2 + -4(x2 + mx2)(9) = 0

Reorder the terms:
4m2x2 + -24mx2 + 36x2 + -4(mx2 + x2)(9) = 0

Reorder the terms for easier multiplication:
4m2x2 + -24mx2 + 36x2 + -4 * 9(mx2 + x2) = 0

Multiply -4 * 9
4m2x2 + -24mx2 + 36x2 + -36(mx2 + x2) = 0
4m2x2 + -24mx2 + 36x2 + (mx2 * -36 + x2 * -36) = 0
4m2x2 + -24mx2 + 36x2 + (-36mx2 + -36x2) = 0

Reorder the terms:
-24mx2 + -36mx2 + 4m2x2 + 36x2 + -36x2 = 0

Combine like terms: -24mx2 + -36mx2 = -60mx2
-60mx2 + 4m2x2 + 36x2 + -36x2 = 0

Combine like terms: 36x2 + -36x2 = 0
-60mx2 + 4m2x2 + 0 = 0
-60mx2 + 4m2x2 = 0

Solving
-60mx2 + 4m2x2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4mx2'.
4mx2(-15 + m) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'mx2' equal to zero and attempt to solve:

Simplifying
mx2 = 0

Solving
mx2 = 0

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

Simplifying
mx2 = 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 '(-15 + m)' equal to zero and attempt to solve:

Simplifying
-15 + m = 0

Solving
-15 + m = 0

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

Add '15' to each side of the equation.
-15 + 15 + m = 0 + 15

Combine like terms: -15 + 15 = 0
0 + m = 0 + 15
m = 0 + 15

Combine like terms: 0 + 15 = 15
m = 15

Simplifying
m = 15
Solution
m = {15}

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