(x+a)(x+b)=x^2+2rx+r^2-s^2

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Solution for (x+a)(x+b)=x^2+2rx+r^2-s^2 equation: 


Simplifying
(x + a)(x + b) = x2 + 2rx + r2 + -1s2

Reorder the terms:
(a + x)(x + b) = x2 + 2rx + r2 + -1s2

Reorder the terms:
(a + x)(b + x) = x2 + 2rx + r2 + -1s2

Multiply (a + x) * (b + x)
(a(b + x) + x(b + x)) = x2 + 2rx + r2 + -1s2
((b * a + x * a) + x(b + x)) = x2 + 2rx + r2 + -1s2
((ab + ax) + x(b + x)) = x2 + 2rx + r2 + -1s2
(ab + ax + (b * x + x * x)) = x2 + 2rx + r2 + -1s2
(ab + ax + (bx + x2)) = x2 + 2rx + r2 + -1s2
(ab + ax + bx + x2) = x2 + 2rx + r2 + -1s2

Reorder the terms:
ab + ax + bx + x2 = 2rx + r2 + -1s2 + x2

Add '-1x2' to each side of the equation.
ab + ax + bx + x2 + -1x2 = 2rx + r2 + -1s2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
ab + ax + bx + 0 = 2rx + r2 + -1s2 + x2 + -1x2
ab + ax + bx = 2rx + r2 + -1s2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
ab + ax + bx = 2rx + r2 + -1s2 + 0
ab + ax + bx = 2rx + r2 + -1s2

Solving
ab + ax + bx = 2rx + r2 + -1s2

Solving for variable 'a'.

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

Add '-1bx' to each side of the equation.
ab + ax + bx + -1bx = 2rx + r2 + -1bx + -1s2

Combine like terms: bx + -1bx = 0
ab + ax + 0 = 2rx + r2 + -1bx + -1s2
ab + ax = 2rx + r2 + -1bx + -1s2

Reorder the terms:
ab + ax = -1bx + 2rx + r2 + -1s2

Reorder the terms:
ab + ax + bx + -2rx + -1r2 + s2 = -1bx + bx + 2rx + -2rx + r2 + -1r2 + -1s2 + s2

Combine like terms: -1bx + bx = 0
ab + ax + bx + -2rx + -1r2 + s2 = 0 + 2rx + -2rx + r2 + -1r2 + -1s2 + s2
ab + ax + bx + -2rx + -1r2 + s2 = 2rx + -2rx + r2 + -1r2 + -1s2 + s2

Combine like terms: 2rx + -2rx = 0
ab + ax + bx + -2rx + -1r2 + s2 = 0 + r2 + -1r2 + -1s2 + s2
ab + ax + bx + -2rx + -1r2 + s2 = r2 + -1r2 + -1s2 + s2

Combine like terms: r2 + -1r2 = 0
ab + ax + bx + -2rx + -1r2 + s2 = 0 + -1s2 + s2
ab + ax + bx + -2rx + -1r2 + s2 = -1s2 + s2

Combine like terms: -1s2 + s2 = 0
ab + ax + bx + -2rx + -1r2 + s2 = 0

The solution to this equation could not be determined.

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