Question 6103
1)
{{{x^2-5x+6=0}}}
Find the 2 middle terms which are the sum of -5x and a product of 6.
{{{x^2-2x-3x+6=0}}}
Now use the factoring by grouping method. 
{{{x(x-2)-3(x-2)=0}}}
Now factor their common term
{{{(x-2)(x-3)=0}}}
Solve for x
(x-2)=0, x=2
(x-3)=0, x=3
2)
{{{2x^2-9x-5=0}}}
Proceed as showed above
{{{2x^2-10x+x-5=0}}}
{{{2x(x-5)+(x-5)=0}}}
{{{(x-5)(2x+1)=0}}}
Solve for x
x-5=0, x=5
(2x+1)=0, x= -1/2
3)
{{{3x^2+5x-2=0}}}
{{{3x^2+6x-x-2=0}}}
{{{3x(x+2)-(x+2)=0}}}
{{{(x+2)(3x-1)=0}}}
Solve for x
x+2=0, x=-2
(3x-1)=0, x=1/3
Hope it helps