(4m+1)x^2-(4n-1)y^2=2015

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Solution for (4m+1)x^2-(4n-1)y^2=2015 equation: 


Simplifying
(4m + 1) * x2 + -1(4n + -1) * y2 = 2015

Reorder the terms:
(1 + 4m) * x2 + -1(4n + -1) * y2 = 2015

Reorder the terms for easier multiplication:
x2(1 + 4m) + -1(4n + -1) * y2 = 2015
(1 * x2 + 4m * x2) + -1(4n + -1) * y2 = 2015

Reorder the terms:
(4mx2 + 1x2) + -1(4n + -1) * y2 = 2015
(4mx2 + 1x2) + -1(4n + -1) * y2 = 2015

Reorder the terms:
4mx2 + 1x2 + -1(-1 + 4n) * y2 = 2015

Reorder the terms for easier multiplication:
4mx2 + 1x2 + -1y2(-1 + 4n) = 2015
4mx2 + 1x2 + (-1 * -1y2 + 4n * -1y2) = 2015

Reorder the terms:
4mx2 + 1x2 + (-4ny2 + 1y2) = 2015
4mx2 + 1x2 + (-4ny2 + 1y2) = 2015

Reorder the terms:
4mx2 + -4ny2 + 1x2 + 1y2 = 2015

Solving
4mx2 + -4ny2 + 1x2 + 1y2 = 2015

Solving for variable 'm'.

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

Add '4ny2' to each side of the equation.
4mx2 + -4ny2 + 1x2 + 4ny2 + 1y2 = 2015 + 4ny2

Reorder the terms:
4mx2 + -4ny2 + 4ny2 + 1x2 + 1y2 = 2015 + 4ny2

Combine like terms: -4ny2 + 4ny2 = 0
4mx2 + 0 + 1x2 + 1y2 = 2015 + 4ny2
4mx2 + 1x2 + 1y2 = 2015 + 4ny2

Add '-1x2' to each side of the equation.
4mx2 + 1x2 + -1x2 + 1y2 = 2015 + 4ny2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
4mx2 + 0 + 1y2 = 2015 + 4ny2 + -1x2
4mx2 + 1y2 = 2015 + 4ny2 + -1x2

Add '-1y2' to each side of the equation.
4mx2 + 1y2 + -1y2 = 2015 + 4ny2 + -1x2 + -1y2

Combine like terms: 1y2 + -1y2 = 0
4mx2 + 0 = 2015 + 4ny2 + -1x2 + -1y2
4mx2 = 2015 + 4ny2 + -1x2 + -1y2

Divide each side by '4x2'.
m = 503.75x-2 + nx-2y2 + -0.25 + -0.25x-2y2

Simplifying
m = 503.75x-2 + nx-2y2 + -0.25 + -0.25x-2y2

Reorder the terms:
m = -0.25 + nx-2y2 + 503.75x-2 + -0.25x-2y2

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