SOLUTION: Could you please help me with this algebra question? Solve for x 12(x-4)-(x+2)=(x+2)(x-4) Thanks for any help!!

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Question 208225: Could you please help me with this algebra question?
Solve for x
12(x-4)-(x+2)=(x+2)(x-4)
Thanks for any help!!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
12(x-4)-(x+2)=(x+2)(x-4)
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multiplying this out you get:
12x - 48 - x - 2 = x^2 -2x - 8
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combining like terms you get:
11x - 50 = x^2 -2x - 8
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subtract 11x and add 50 to both sides of this equation to get:
0 = x^2 -2x - 8 + 50 - 11x which is the same as:
x^2 -2x - 8 + 50 - 11x = 0
combine like terms to get:
x^2 - 13x + 42 = 0
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since 7+6 = 13 and 7*6 = 42, you have some factors that you can use.
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x^2 - 13x + 42 = 0 is the same as (x-6)*(x-7) = 0 after you factor it out.
your answer is:
x = 6
or
x = 7
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to prove these numbers are correct, go back to the original equation and replace x with these values to see if the equations are true.
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let x = 6
12(x-4)-(x+2)=(x+2)(x-4) becomes:
12*2 - 8 = (8*2) becomes:
24-8 = 16 becomes:
16 = 16 which is true so the value of 6 for x is good.
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let x = 7
12(x-4)-(x+2)=(x+2)(x-4) becomes:
12*3 - 9 = 9*3 becomes:
36 - 9 = 27 becomes
27 - 27 which is also true so the value of 7 for x is also good.
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answer is confirmed and is:
x = 6
or
x = 7
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