If x units of a product cost c dollars
to manufacture and earn revenue of r
dollars, the value of x where the
expressions of c and r are equal is
called the break-even quantity, the
number of units that produce zero
profit. Find break-even quantity if
c=13x + 20000 and r=15x. 

1. Finst look at the words which tell
you what you are to find.  They are the
words I have made red below:

If x units of a product cost c dollars
to manufacture and earn revenue of r
dollars, the value of x where the
expressions of c and r are equal is
called the break-even quantity, the
number of units that produce zero
profit. Find break-even quantity if
c=13x + 20000 and r=15x.

2. So now we know what to find, the
break-even quantity.  So we look
through the words and find what the
instructions are to find the break
-even quantity.  They are the words I
have made red this time:

If x units of a product cost c dollars
to manufacture and earn revenue of r
dollars, the value of x where the
expressions of c and r are equal is
called the break-even quantity, the
number of units that produce zero
profit. Find break-even quantity if
c=13x + 20000 and r=15x.

3. We look at those red words and
notice in particular the ones I have
made bold and underlined below:

If x units of a product cost c dollars
to manufacture and earn revenue of r
dollars, the value of x where the
expressions of c and r are equal is
called the break-even quantity, the
number of units that produce zero
profit. Find break-even quantity if
c=13x + 20000 and r=15x.

When the words tell us that two things
are equal we write them down side by
side and put an equal sign " = "
between them, like this:

the expressions of c =  the expression of r

Next we look through the words for the
expression of c and the expression of
r.  They are the ones I have made red
below:

If x units of a product cost c dollars 
to manufacture and earn revenue of r 
dollars, the value of x where the 
expressions of c and r are equal is 
called the break-even quantity, the 
number of units that produce zero 
profit. Find break-even 
quantity if 
c=13x + 20000 and r=15x

We notice that the expression for c is
13x + 20000 and the expression for r is
15x.  So instead of

the expressions of c =  the expression of r

we write 

 13x + 20000 = 15x

We subtract 20000 from both sides:

 13x + 20000 = 15x
     - 20000       - 20000
 ------------------------- 
 13x         = 15x - 20000

We subtract 15x from both sides

 13x + 20000 = 15x
     - 20000       - 20000
 ------------------------- 
 13x         = 15x - 20000
-15x          -15x    
 -------------------------
 -2x         =     - 20000

 We divide both sides by the
coefficient of x which is -2

 13x + 20000 = 15x
     - 20000       - 20000
 ------------------------- 
 13x         = 15x - 20000
-15x          -15x    
 -------------------------
 -2x         =     - 20000

 -2x                -20000
-----        =      ------
 -2                    -2

And we cancel the -2's on the left
side and divide on the right side
and get

   x         =       10000

That's the answer: x = 10000.

Edwin