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

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


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

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

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

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

Combine like terms: -12mn + -12mn = -24mn
0 = (-24mn + 16m2 + 9n2)

Solving
0 = -24mn + 16m2 + 9n2

Solving for variable 'm'.
Remove the zero:
24mn + -16m2 + -9n2 = -24mn + 16m2 + 9n2 + 24mn + -16m2 + -9n2

Reorder the terms:
24mn + -16m2 + -9n2 = -24mn + 24mn + 16m2 + -16m2 + 9n2 + -9n2

Combine like terms: -24mn + 24mn = 0
24mn + -16m2 + -9n2 = 0 + 16m2 + -16m2 + 9n2 + -9n2
24mn + -16m2 + -9n2 = 16m2 + -16m2 + 9n2 + -9n2

Combine like terms: 16m2 + -16m2 = 0
24mn + -16m2 + -9n2 = 0 + 9n2 + -9n2
24mn + -16m2 + -9n2 = 9n2 + -9n2

Combine like terms: 9n2 + -9n2 = 0
24mn + -16m2 + -9n2 = 0

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


Subproblem 1
Set the factor '(-4m + 3n)' equal to zero and attempt to solve:

Simplifying
-4m + 3n = 0

Solving
-4m + 3n = 0

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

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

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

Divide each side by '-4'.
m = 0.75n

Simplifying
m = 0.75n

Subproblem 2
Set the factor '(4m + -3n)' equal to zero and attempt to solve:

Simplifying
4m + -3n = 0

Solving
4m + -3n = 0

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

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

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

Divide each side by '4'.
m = 0.75n

Simplifying
m = 0.75n
Solution
m = {0.75n, 0.75n}

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