[x-(a+b)][x+(a-b)]=0

Solution for [x-(a+b)][x+(a-b)]=0 equation:

Simplifying
[x + -1(a + b)][x + (a + -1b)] = 0
[x + (a * -1 + b * -1)][x + (a + -1b)] = 0
[x + (-1a + -1b)][x + (a + -1b)] = 0

Reorder the terms:
[-1a + -1b + x][x + (a + -1b)] = 0

Remove parenthesis around (a + -1b)
[-1a + -1b + x][x + a + -1b] = 0

Reorder the terms:
[-1a + -1b + x][a + -1b + x] = 0

Multiply [-1a + -1b + x] * [a + -1b + x]
[-1a * [a + -1b + x] + -1b * [a + -1b + x] + x[a + -1b + x]] = 0
[[a * -1a + -1b * -1a + x * -1a] + -1b * [a + -1b + x] + x[a + -1b + x]] = 0

Reorder the terms:
[[1ab + -1ax + -1a2] + -1b * [a + -1b + x] + x[a + -1b + x]] = 0
[[1ab + -1ax + -1a2] + -1b * [a + -1b + x] + x[a + -1b + x]] = 0
[1ab + -1ax + -1a2 + [a * -1b + -1b * -1b + x * -1b] + x[a + -1b + x]] = 0

Reorder the terms:
[1ab + -1ax + -1a2 + [-1ab + -1bx + 1b2] + x[a + -1b + x]] = 0
[1ab + -1ax + -1a2 + [-1ab + -1bx + 1b2] + x[a + -1b + x]] = 0
[1ab + -1ax + -1a2 + -1ab + -1bx + 1b2 + [a * x + -1b * x + x * x]] = 0
[1ab + -1ax + -1a2 + -1ab + -1bx + 1b2 + [ax + -1bx + x2]] = 0

Reorder the terms:
[1ab + -1ab + -1ax + ax + -1a2 + -1bx + -1bx + 1b2 + x2] = 0

Combine like terms: 1ab + -1ab = 0
[0 + -1ax + ax + -1a2 + -1bx + -1bx + 1b2 + x2] = 0
[-1ax + ax + -1a2 + -1bx + -1bx + 1b2 + x2] = 0

Combine like terms: -1ax + ax = 0
[0 + -1a2 + -1bx + -1bx + 1b2 + x2] = 0
[-1a2 + -1bx + -1bx + 1b2 + x2] = 0

Combine like terms: -1bx + -1bx = -2bx
[-1a2 + -2bx + 1b2 + x2] = 0

Solving
-1a2 + -2bx + 1b2 + x2 = 0

Solving for variable 'a'.

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

Add '2bx' to each side of the equation.
-1a2 + -2bx + 1b2 + 2bx + x2 = 0 + 2bx

Reorder the terms:
-1a2 + -2bx + 2bx + 1b2 + x2 = 0 + 2bx

Combine like terms: -2bx + 2bx = 0
-1a2 + 0 + 1b2 + x2 = 0 + 2bx
-1a2 + 1b2 + x2 = 0 + 2bx
Remove the zero:
-1a2 + 1b2 + x2 = 2bx

Add '-1b2' to each side of the equation.
-1a2 + 1b2 + -1b2 + x2 = 2bx + -1b2

Combine like terms: 1b2 + -1b2 = 0
-1a2 + 0 + x2 = 2bx + -1b2
-1a2 + x2 = 2bx + -1b2

Add '-1x2' to each side of the equation.
-1a2 + x2 + -1x2 = 2bx + -1b2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1a2 + 0 = 2bx + -1b2 + -1x2
-1a2 = 2bx + -1b2 + -1x2

Divide each side by '-1'.
a2 = -2bx + b2 + x2

Simplifying
a2 = -2bx + b2 + x2

Reorder the terms:
a2 + 2bx + -1b2 + -1x2 = -2bx + 2bx + b2 + -1b2 + x2 + -1x2

Combine like terms: -2bx + 2bx = 0
a2 + 2bx + -1b2 + -1x2 = 0 + b2 + -1b2 + x2 + -1x2
a2 + 2bx + -1b2 + -1x2 = b2 + -1b2 + x2 + -1x2

Combine like terms: b2 + -1b2 = 0
a2 + 2bx + -1b2 + -1x2 = 0 + x2 + -1x2
a2 + 2bx + -1b2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
a2 + 2bx + -1b2 + -1x2 = 0

The solution to this equation could not be determined.