To solve this equation you must have more information.  Because there is both x and y variables there will be a range of answers for both.  If it is a quadratic equation the y has a 0 value.  Then you can begin the process of factoring and finding the solutions.

0=2x^2+12x+10

0=2(x^2+6x+5)

The two is eliminated.

0=(x+5)(x+1)

x+5=0

x=-5

x+1=0

x=-1

x=-1,-5

Problem: y=2x²+12x+10

Step 1: Factor out common number that is shared by each of the terms. Basically in this step we are trying to get rid of the coefficient in front of the x² so we can simplify the quadratic eqn and in turn factor easily. 

              y=2(x²+6x+5)

Step 2: factor the polynomial inside the parenthesis

              x²+6x+5 becomes or is equal to (x+5)(x+1)

           Hence: y=2((x+5)(x+1))

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If this problem asks what x would be if y=0, then the following step is your solution. Otherwise, the simplified form is a factored solution. 

Step 3: y=0

           0=2((x+5)(x+1))

           0=(x+5)(x+1) --> In multiplication, if either or both of the numbers were to be 0, the  

                                     product is 0. (Eg. 2*0=0....or....0*0=0)

                                     So have (x+5)=0 and (x+1)=0

                                           Then x=-5    and x=-1