(6m-3n)(6m-3n)=0

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Solution for (6m-3n)(6m-3n)=0 equation: 


Simplifying
(6m + -3n)(6m + -3n) = 0

Multiply (6m + -3n) * (6m + -3n)
(6m * (6m + -3n) + -3n * (6m + -3n)) = 0
((6m * 6m + -3n * 6m) + -3n * (6m + -3n)) = 0

Reorder the terms:
((-18mn + 36m2) + -3n * (6m + -3n)) = 0
((-18mn + 36m2) + -3n * (6m + -3n)) = 0
(-18mn + 36m2 + (6m * -3n + -3n * -3n)) = 0
(-18mn + 36m2 + (-18mn + 9n2)) = 0

Reorder the terms:
(-18mn + -18mn + 36m2 + 9n2) = 0

Combine like terms: -18mn + -18mn = -36mn
(-36mn + 36m2 + 9n2) = 0

Solving
-36mn + 36m2 + 9n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-4mn + 4m2 + n2) = 0

Factor a trinomial.
9((2m + -1n)(2m + -1n)) = 0

Ignore the factor 9.

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

Simplifying
2m + -1n = 0

Solving
2m + -1n = 0

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

Add 'n' to each side of the equation.
2m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
2m + 0 = 0 + n
2m = 0 + n
Remove the zero:
2m = n

Divide each side by '2'.
m = 0.5n

Simplifying
m = 0.5n

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

Simplifying
2m + -1n = 0

Solving
2m + -1n = 0

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

Add 'n' to each side of the equation.
2m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
2m + 0 = 0 + n
2m = 0 + n
Remove the zero:
2m = n

Divide each side by '2'.
m = 0.5n

Simplifying
m = 0.5n
Solution
m = {0.5n, 0.5n}

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