1.

x²+2x=16x-49

x²-14x+49=0

x²-7x-7x+49=0

x(x-7)-7(x-7)=0

(x-7)(x-7)=0

(x-7)²=0

x=7

2.

x(2x+1)=3x+4

2x²+x=3x+4

2x²-2x-4=0

x²-x-2=0

x²+x-2x-2=0

x(x+1)-2(x+1)=0

(x-2)(x+1)=0

x=2 ∨ x=-1

3.

6/(x+5)=4/(3-4)  ⇐ 3-4 ???

4.

6/x+6/(x+1)=5 |*x(x+1)

6(x+1)+6x=5x(x+1)
6x+6+6x=5x²+5x

5x²-7x-6=0

5x²-10x+3x-6=0

5x(x-2)+3(x-2)=0

(5x+3)(x-2)=0

5x+3=0

5x=-3

x=-3/5 ∨ x=2