(5x²-6x+1=0)
(5x²-6x+1=(5x-1)(x-1) = 0)
(x = \frac{1}{5}) or (x = 1)

(4x²-36x+77=0)
(4x²-36x+77=(2x-7)(2x-11)=0)
(x = \frac{7}{2}) or (x = \frac{11}{2})

(x²-22x-23=0)
(x²-22x-23=(x-23)(x+1)=0)
(x = 23) or (x = -1)

(5x+(2x+1)(x-3)=0)
(5x+(2x+1)(x-3)=5x+(2x²-5x-3)=5x+2x²-5x-3=2x²-3=0)
(^2-3=(x-3)(x+1)=0)
(x = 3) or (x = -1)

((2x+3)(3x+1)=11x+30)
(2x·3x+2x·1+3x·3+3·1 = 11x+30)
(6x²+2x+9x+3 = 11x+30)
(6x²+11x+3 = 11x+30)
(6x² = 11x+27)
This is an identity, not an equation to solve.