(2m+3n)(2m-3n)=0

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Solution for (2m+3n)(2m-3n)=0 equation: 


Simplifying
(2m + 3n)(2m + -3n) = 0

Multiply (2m + 3n) * (2m + -3n)
(2m * (2m + -3n) + 3n * (2m + -3n)) = 0
((2m * 2m + -3n * 2m) + 3n * (2m + -3n)) = 0

Reorder the terms:
((-6mn + 4m2) + 3n * (2m + -3n)) = 0
((-6mn + 4m2) + 3n * (2m + -3n)) = 0
(-6mn + 4m2 + (2m * 3n + -3n * 3n)) = 0
(-6mn + 4m2 + (6mn + -9n2)) = 0

Reorder the terms:
(-6mn + 6mn + 4m2 + -9n2) = 0

Combine like terms: -6mn + 6mn = 0
(0 + 4m2 + -9n2) = 0
(4m2 + -9n2) = 0

Solving
4m2 + -9n2 = 0

Solving for variable 'm'.

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

Add '9n2' to each side of the equation.
4m2 + -9n2 + 9n2 = 0 + 9n2

Combine like terms: -9n2 + 9n2 = 0
4m2 + 0 = 0 + 9n2
4m2 = 0 + 9n2
Remove the zero:
4m2 = 9n2

Divide each side by '4'.
m2 = 2.25n2

Simplifying
m2 = 2.25n2

Take the square root of each side:
m = {-1.5n, 1.5n}

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