Question 92994
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Solve:          2x(x+3)= x + 25

Distribute the 2x:

              2x² + 6x = x + 25

Get 0 on the right and the left side in descending
order of powers of x:
 
         <font color = "red">2</font>x² + <font color = "blue">5</font>x - <font color = "green">25</font> = 0

Multiply the <font color = "red">2</font> by the <font color = "green">25</font>, getting 50.
Think of two positive integers, which have DIFFERENCE*** <font color = "blue">5</font>.
These are 10 and 5.  So use 10 and 5 to rewrite the
middle term <font color = "blue">5</font>x as <font color = "indigo">10x - 5x</font>.

   2x² + <font color = "indigo">10x - 5x</font> - 25 = 0

Factor the first two terms 2x² + 10x as 2x(x+5)
Factor the last two terms -5x-25 as -5(x+5)
  
         2x(x+5) - 5(x+5) = 0

Factor out the parentheses (x+5) which leaves the 2x in the 
first term and -5 in the second to put in another set of parentheses:

            (x+5)(2x - 5) = 0

Set each factor = 0

x+5=0 gives solution x=-5

2x-5=0 gives solution x={{{5/2}}}        
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***<font size = 2>Footnote: This is DIFFERENCE because the last sign is 
MINUS.  When the last sign is PLUS, this would be SUM.
Edwin</pre>