Three times the square of a non zero number is equal to 15 times the number

First we have to write these words in math. This now looks like 3x^2 = 15x.  We can also write this as 3x^2 - 15x = 0.  This looks like a quadratic, and it is!  We can factor this quadratic into the product of two binomials, or (3x + 0)(x - 15).

In order to make (3x)(x - 15) equal to 0, either (3x) or (x-15) has to be equal to zero. This is because the product of a number and 0 always equals the number 0.

If 3x = 0, x needs to equal 0. But because x is a non zero number, x can't be zero.

Moving on to x-15 = 0, we see that x can equal 15.  So the two possible values of x in our equation (3x)(x-15) are 0 and 15.  We can eliminate 0 because x is a non zero number to get 15 as our final value for x.