X(x-2b)/(x+b)(x+5)=0

Solve x(x − 2b) / [(x + b)(x + 5)] = 0. - The fraction is zero when the numerator is zero (and the denominator is nonzero). - So x(x − 2b) = 0 → x = 0 or x = 2b. Domain restrictions: x ≠ −b and x ≠ −5. Check each root: - x = 0 is allowed if 0 ≠ −b, i.e., b ≠ 0. - x = 2b is allowed if 2b ≠ −b (i.e., b ≠ 0) and 2b ≠ −5 (i.e., b ≠ −5/2). Special cases: - If b = 0: no solutions (denominator is zero at x = 0, and the equation is undefined there). - If b = −5/2: x = 0 is valid, but x = 2b = −5 is not (denominator zero at x = −5). Summary: - If b ≠ 0 and b ≠ −5/2: x = 0 and x = 2b are solutions. - If b = −5/2: x = 0 is the only solution. - If b = 0: no solution.