To solve this equation, first expand the expressions:

(x-7)(x+3) = x^2 - 7x + 3x - 21 = x^2 - 4x - 21
(x-1)(x+5) = x^2 - x + 5x - 5 = x^2 + 4x - 5

Now, substitute these expanded expressions back into the original equation:

(x^2 - 4x - 21) + (x^2 + 4x - 5) + 26 = 0
2x^2 - 26 = 0

Now, solve for x:

2x^2 = 26
x^2 = 13
x = ±√13

Therefore, the solutions to the equation are x = √13 and x = -√13.