# SOLUTION: Solve: 2x(x+3)= x + 25

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 Click here to see ALL problems on Equations Question 92994: Solve: 2x(x+3)= x + 25Answer by Edwin McCravy(8880)   (Show Source): You can put this solution on YOUR website!``` 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: 2x² + 5x - 25 = 0 Multiply the 2 by the 25, getting 50. Think of two positive integers, which have DIFFERENCE*** 5. These are 10 and 5. So use 10 and 5 to rewrite the middle term 5x as 10x - 5x. 2x² + 10x - 5x - 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= ------------------------------------------------------- ***Footnote: This is DIFFERENCE because the last sign is MINUS. When the last sign is PLUS, this would be SUM. Edwin```