How do I solve the following problems??

Question

1. Factor: 4x^2-100y^2

2. Factor: 3x^2+27

3. Solve 3x^2+9x=0

4. Solve 12^2+30x=-12

5. 9a(a+1)=4

6. Solve 16x^2=25

Answer 1

Hints:

1. Factor: 4x^2-100y^2
use difference of two squares,
(a²-b²)=(a+b)(a-b)

2. Factor: 3x^2+27
the common factor is 3.

3. Solve 3x^2+9x=0
factor and solve:
3x(x+3)=0
therefore
x=0 or x=?

4. Solve 12^2+30x=-12
Factor out the 6, and then factor completely to solve for x:
6(2x²+5x+2)=0
Hint: it's in the form
(2x 1)(x 2)

5. 9a(a+1)=4
Expand, transpose everything to the left, and then factor.
9a²+9a-4=0

6. Solve 16x^2=25
isolate variable:
x²=(25/16)=(5/4)²
and solve for x.