Type 1: Biquadratic ax^4 + bx^2 + c = 0 Substitute t = x^2. Solve for t, then x = ±sqrt(t). Only t >= 0 gives real x.

Type 2: Reciprocal ax^4 + bx^3 + cx^2 + bx + a = 0 Divide by x^2: a(x^2+1/x^2) + b(x+1/x) + c = 0. Substitute t = x+1/x, so x^2+1/x^2 = t^2-2.

Type 3: Equation with sqrt sqrt(f(x)) = g(x). Square both sides: f(x) = [g(x)]^2. But must verify g(x) >= 0 and f(x) >= 0.

Type 4: Exponential a^(2x) + b*a^x + c = 0 Substitute t = a^x (t > 0). Solve quadratic in t, then x = log_a(t).