Question 4718
1)  4x^2+12x+9=0
(2x+3)(2x+3)=0
2x+3=0
2x=-3
x=-3/2

2)  7(x+2)^2=12
7(x^2+4x+4)=12
7x^2+28x+28=12
Subtract 28 from both sides:
7x^2+28x=-16
Divide by 7 and complete the square:
x^2+4x=-16/7
(x+2)^2=-16/7+4
{{{x+2 = ( +- sqrt( 12/7 ))}}}
{{{x=-2+sqrt(12/7)}}},{{{ x=-2-sqrt(12/7)}}}

3)  2x^2-8x+5=0
Subtract 5 from both sides and Divide by 2 and complete the square:
x^2-4x=-5/2
(x-2)^2=-5/2+4
{{{x-2 = ( +- sqrt( 3/2 ))}}}
{{{x=2+sqrt(3/2)}}},{{{ x=-2-sqrt(3/2)}}}


4)  (2x-5)/(x-3)=(4x+1)/(2x)
Multiply both sides by (2x)(x-3)
(2x-5)(2x)=(4x+1)(x-3)
simplify
{{{4x^2-10x=4x^2-12x+x-3}}}
Subtract {{{4x^2}}} from both sides
-10x=-11x-3
Add 11x to both sides
x=-3