(p^2-q^2)z=x-y

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Solution for (p^2-q^2)z=x-y equation:


Simplifying
(p2 + -1q2) * z = x + -1y

Reorder the terms for easier multiplication:
z(p2 + -1q2) = x + -1y
(p2 * z + -1q2 * z) = x + -1y
(p2z + -1q2z) = x + -1y

Solving
p2z + -1q2z = x + -1y

Solving for variable 'p'.

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

Add 'q2z' to each side of the equation.
p2z + -1q2z + q2z = x + q2z + -1y

Combine like terms: -1q2z + q2z = 0
p2z + 0 = x + q2z + -1y
p2z = x + q2z + -1y

Reorder the terms:
p2z = q2z + x + -1y

Divide each side by 'z'.
p2 = q2 + xz-1 + -1yz-1

Simplifying
p2 = q2 + xz-1 + -1yz-1

Reorder the terms:
p2 + -1q2 + -1xz-1 + yz-1 = q2 + -1q2 + xz-1 + -1xz-1 + -1yz-1 + yz-1

Combine like terms: q2 + -1q2 = 0
p2 + -1q2 + -1xz-1 + yz-1 = 0 + xz-1 + -1xz-1 + -1yz-1 + yz-1
p2 + -1q2 + -1xz-1 + yz-1 = xz-1 + -1xz-1 + -1yz-1 + yz-1

Combine like terms: xz-1 + -1xz-1 = 0
p2 + -1q2 + -1xz-1 + yz-1 = 0 + -1yz-1 + yz-1
p2 + -1q2 + -1xz-1 + yz-1 = -1yz-1 + yz-1

Combine like terms: -1yz-1 + yz-1 = 0
p2 + -1q2 + -1xz-1 + yz-1 = 0

The solution to this equation could not be determined.

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