In a quadratic in the form #ax^2+bx+c#, find two numbers that multiply to #a*c# and add up to #b# in order to factor.
In this case, we need two numbers that multiply to #6# and add up to #-5#. These two numbers are #-2# and #-3#.
Now, split up the #x# term into these two numbers. Next, factor the first two terms and the last two terms separately, then combine them. Lastly, set each factor equal to zero and solve for #x# in each one. Here's what all that looks like:
#x^2-5x+6=0#
#x^2-2x-3x+6=0#
#color(red)x(x-2)-3x+6=0#
#color(red)x(x-2)color(blue)-color(blue)3(x-2)=0#
#(color(red)xcolor(blue)-color(blue)3)(x-2)=0#
#color(white){color(black)(
(x-3=0,qquadx-2=0),
(x=3,qquadx=2):}#
These are the two solutions. Hope this helped!
