Question 242608
Let the two numbers be represented by x and y
You are told " When they are multiplied, the product is 36, when they are added, the sum is 15, what are the two numbers?"
So
{{{x * y = 36}}}


{{{x + y = 15}}} isolate x
{{{x = 15-y}}} use this value for x in the first equation


{{{x * y = 36}}}
{{{(15-y)*y = 36}}} expand
{{{15y - y^2 = 36}}} collect into quadratic form
{{{0 = y^2 -15y +36}}} factor
{{{0 = (y-3)(y-12)}}} For a product to be zero,one or more factors must be 0
So
{{{y-3=0}}} or {{{y-12=0}}}
y = 3  or y = 12

The two numbers are 3 and 12