(3m-4n)x(3m-4n)=

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Solution for (3m-4n)x(3m-4n)= equation: 


Simplifying
(3m + -4n) * x(3m + -4n) = 0

Reorder the terms for easier multiplication:
x(3m + -4n)(3m + -4n) = 0

Multiply (3m + -4n) * (3m + -4n)
x(3m * (3m + -4n) + -4n * (3m + -4n)) = 0
x((3m * 3m + -4n * 3m) + -4n * (3m + -4n)) = 0

Reorder the terms:
x((-12mn + 9m2) + -4n * (3m + -4n)) = 0
x((-12mn + 9m2) + -4n * (3m + -4n)) = 0
x(-12mn + 9m2 + (3m * -4n + -4n * -4n)) = 0
x(-12mn + 9m2 + (-12mn + 16n2)) = 0

Reorder the terms:
x(-12mn + -12mn + 9m2 + 16n2) = 0

Combine like terms: -12mn + -12mn = -24mn
x(-24mn + 9m2 + 16n2) = 0
(-24mn * x + 9m2 * x + 16n2 * x) = 0
(-24mnx + 9m2x + 16n2x) = 0

Solving
-24mnx + 9m2x + 16n2x = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24mn + 9m2 + 16n2) = 0

Factor a trinomial.
x((3m + -4n)(3m + -4n)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

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 '(3m + -4n)' equal to zero and attempt to solve:

Simplifying
3m + -4n = 0

Solving
3m + -4n = 0

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

Add '4n' to each side of the equation.
3m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
3m + 0 = 0 + 4n
3m = 0 + 4n
Remove the zero:
3m = 4n

Divide each side by '3'.
m = 1.333333333n

Simplifying
m = 1.333333333n

Subproblem 3
Set the factor '(3m + -4n)' equal to zero and attempt to solve:

Simplifying
3m + -4n = 0

Solving
3m + -4n = 0

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

Add '4n' to each side of the equation.
3m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
3m + 0 = 0 + 4n
3m = 0 + 4n
Remove the zero:
3m = 4n

Divide each side by '3'.
m = 1.333333333n

Simplifying
m = 1.333333333n
Solution
m = {1.333333333n, 1.333333333n}

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