(x+a)(x-a)-x(x+b)=c

Solution for (x+a)(x-a)-x(x+b)=c equation:

Simplifying
(x + a)(x + -1a) + -1x(x + b) = c

Reorder the terms:
(a + x)(x + -1a) + -1x(x + b) = c

Reorder the terms:
(a + x)(-1a + x) + -1x(x + b) = c

Multiply (a + x) * (-1a + x)
(a(-1a + x) + x(-1a + x)) + -1x(x + b) = c
((-1a * a + x * a) + x(-1a + x)) + -1x(x + b) = c

Reorder the terms:
((ax + -1a2) + x(-1a + x)) + -1x(x + b) = c
((ax + -1a2) + x(-1a + x)) + -1x(x + b) = c
(ax + -1a2 + (-1a * x + x * x)) + -1x(x + b) = c
(ax + -1a2 + (-1ax + x2)) + -1x(x + b) = c

Reorder the terms:
(ax + -1ax + -1a2 + x2) + -1x(x + b) = c

Combine like terms: ax + -1ax = 0
(0 + -1a2 + x2) + -1x(x + b) = c
(-1a2 + x2) + -1x(x + b) = c

Reorder the terms:
-1a2 + x2 + -1x(b + x) = c
-1a2 + x2 + (b * -1x + x * -1x) = c
-1a2 + x2 + (-1bx + -1x2) = c

Reorder the terms:
-1a2 + -1bx + x2 + -1x2 = c

Combine like terms: x2 + -1x2 = 0
-1a2 + -1bx + 0 = c
-1a2 + -1bx = c

Solving
-1a2 + -1bx = c

Solving for variable 'a'.

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

Add 'bx' to each side of the equation.
-1a2 + -1bx + bx = bx + c

Combine like terms: -1bx + bx = 0
-1a2 + 0 = bx + c
-1a2 = bx + c

Divide each side by '-1'.
a2 = -1bx + -1c

Simplifying
a2 = -1bx + -1c

Reorder the terms:
a2 + bx + c = -1bx + bx + -1c + c

Combine like terms: -1bx + bx = 0
a2 + bx + c = 0 + -1c + c
a2 + bx + c = -1c + c

Combine like terms: -1c + c = 0
a2 + bx + c = 0

The solution to this equation could not be determined.