(x-p)(x-q)=(r-p)(r-q)

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Solution for (x-p)(x-q)=(r-p)(r-q) equation: 


Simplifying
(x + -1p)(x + -1q) = (r + -1p)(r + -1q)

Reorder the terms:
(-1p + x)(x + -1q) = (r + -1p)(r + -1q)

Reorder the terms:
(-1p + x)(-1q + x) = (r + -1p)(r + -1q)

Multiply (-1p + x) * (-1q + x)
(-1p * (-1q + x) + x(-1q + x)) = (r + -1p)(r + -1q)
((-1q * -1p + x * -1p) + x(-1q + x)) = (r + -1p)(r + -1q)
((1pq + -1px) + x(-1q + x)) = (r + -1p)(r + -1q)
(1pq + -1px + (-1q * x + x * x)) = (r + -1p)(r + -1q)
(1pq + -1px + (-1qx + x2)) = (r + -1p)(r + -1q)
(1pq + -1px + -1qx + x2) = (r + -1p)(r + -1q)

Reorder the terms:
1pq + -1px + -1qx + x2 = (-1p + r)(r + -1q)

Reorder the terms:
1pq + -1px + -1qx + x2 = (-1p + r)(-1q + r)

Multiply (-1p + r) * (-1q + r)
1pq + -1px + -1qx + x2 = (-1p * (-1q + r) + r(-1q + r))
1pq + -1px + -1qx + x2 = ((-1q * -1p + r * -1p) + r(-1q + r))
1pq + -1px + -1qx + x2 = ((1pq + -1pr) + r(-1q + r))
1pq + -1px + -1qx + x2 = (1pq + -1pr + (-1q * r + r * r))
1pq + -1px + -1qx + x2 = (1pq + -1pr + (-1qr + r2))
1pq + -1px + -1qx + x2 = (1pq + -1pr + -1qr + r2)

Add '-1pq' to each side of the equation.
1pq + -1px + -1qx + -1pq + x2 = 1pq + -1pr + -1qr + -1pq + r2

Reorder the terms:
1pq + -1pq + -1px + -1qx + x2 = 1pq + -1pr + -1qr + -1pq + r2

Combine like terms: 1pq + -1pq = 0
0 + -1px + -1qx + x2 = 1pq + -1pr + -1qr + -1pq + r2
-1px + -1qx + x2 = 1pq + -1pr + -1qr + -1pq + r2

Reorder the terms:
-1px + -1qx + x2 = 1pq + -1pq + -1pr + -1qr + r2

Combine like terms: 1pq + -1pq = 0
-1px + -1qx + x2 = 0 + -1pr + -1qr + r2
-1px + -1qx + x2 = -1pr + -1qr + r2

Solving
-1px + -1qx + x2 = -1pr + -1qr + r2

Solving for variable 'p'.

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

Add 'pr' to each side of the equation.
-1px + -1qx + pr + x2 = -1pr + -1qr + pr + r2

Reorder the terms:
pr + -1px + -1qx + x2 = -1pr + -1qr + pr + r2

Reorder the terms:
pr + -1px + -1qx + x2 = -1pr + pr + -1qr + r2

Combine like terms: -1pr + pr = 0
pr + -1px + -1qx + x2 = 0 + -1qr + r2
pr + -1px + -1qx + x2 = -1qr + r2

Add 'qx' to each side of the equation.
pr + -1px + -1qx + qx + x2 = -1qr + qx + r2

Combine like terms: -1qx + qx = 0
pr + -1px + 0 + x2 = -1qr + qx + r2
pr + -1px + x2 = -1qr + qx + r2

Add '-1x2' to each side of the equation.
pr + -1px + x2 + -1x2 = -1qr + qx + r2 + -1x2

Combine like terms: x2 + -1x2 = 0
pr + -1px + 0 = -1qr + qx + r2 + -1x2
pr + -1px = -1qr + qx + r2 + -1x2

Reorder the terms:
pr + -1px + qr + -1qx + -1r2 + x2 = -1qr + qr + qx + -1qx + r2 + -1r2 + -1x2 + x2

Combine like terms: -1qr + qr = 0
pr + -1px + qr + -1qx + -1r2 + x2 = 0 + qx + -1qx + r2 + -1r2 + -1x2 + x2
pr + -1px + qr + -1qx + -1r2 + x2 = qx + -1qx + r2 + -1r2 + -1x2 + x2

Combine like terms: qx + -1qx = 0
pr + -1px + qr + -1qx + -1r2 + x2 = 0 + r2 + -1r2 + -1x2 + x2
pr + -1px + qr + -1qx + -1r2 + x2 = r2 + -1r2 + -1x2 + x2

Combine like terms: r2 + -1r2 = 0
pr + -1px + qr + -1qx + -1r2 + x2 = 0 + -1x2 + x2
pr + -1px + qr + -1qx + -1r2 + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
pr + -1px + qr + -1qx + -1r2 + x2 = 0

The solution to this equation could not be determined.

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