>keep separating and factoring one of the terms until a unit variable is left(.i.e 3x+2y=5 => x+2(x+y)=5)
>isolate unit variable on one side
>set variable expression on other side equal to k, hence get one of the variables in the form of k
>find the other variable in terms of k by substituting the value of one of the variable in terms of k in the main equation
>set both x,y in terms of k equations to be greater than zero
>k will be between two rationals, and all integers in that interval are eligible values of k
>substitute values of k to find the pair of x and y that are solutions
>hence find all natural solutions for x and y
>isolate unit variable on one side
>set variable expression on other side equal to k, hence get one of the variables in the form of k
>find the other variable in terms of k by substituting the value of one of the variable in terms of k in the main equation
>set both x,y in terms of k equations to be greater than zero
>k will be between two rationals, and all integers in that interval are eligible values of k
>substitute values of k to find the pair of x and y that are solutions
>hence find all natural solutions for x and y
