Answer:

1.

2x^2-6x=0

2x(x-3)=0 (Factorise the equation)

2x=0 OR x-3=0 (Zero product rule)

x=0 OR x=3

2.

x^2+22x+121=0

(x+11)(x+11)=0 (Factorise the equation)

x+11=0 OR x+11=0 (Zero product rule)

x=-11

3.

x^2-625=0

x^2=625

x^2=

     = 25 OR -25

4.

4a^2+9a=9

4a^2+9a-9=0 (Equate the equation to zero)

(4a−3)(a+3)=0 (Factorise the equation)

4a-3=0 OR a+3=0 (Zero product rule)

4a=3 OR a=-3

a= 3/4 OR a=-3

5.

2(3a^2-5)=8a+4

6a^2-10=8a+4 (Expand the expression)

6a^2-10-8a-4=0 (Equate the equation to zero)

6a^2-8a-14=0

2(3a^2-4a-7)=0 (Simplify)

(3a−7)(a+1)=0 (Factorise the equation)

3a-7=0 OR a+1=0 (Zero product rule)

3a=7 OR a=-1

a= 7/3 OR a=-1

Hope this helped! :>