(x+5)*(5-x)=(12+x)*(4-x)+1

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Solution for (x+5)*(5-x)=(12+x)*(4-x)+1 equation: 



(x+5)(5-x)=(12+x)(4-x)+1

We move all terms to the left:

(x+5)(5-x)-((12+x)(4-x)+1)=0

We add all the numbers together, and all the variables

(x+5)(-1x+5)-((x+12)(-1x+4)+1)=0

We multiply parentheses ..

(-1x^2+5x-5x+25)-((x+12)(-1x+4)+1)=0



We calculate terms in parentheses: -((x+12)(-1x+4)+1), so:

(x+12)(-1x+4)+1

We multiply parentheses ..

(-1x^2+4x-12x+48)+1

We get rid of parentheses

-1x^2+4x-12x+48+1

We add all the numbers together, and all the variables

-1x^2-8x+49

Back to the equation:

-(-1x^2-8x+49)



We get rid of parentheses

-1x^2+1x^2+5x-5x+8x+25-49=0

We add all the numbers together, and all the variables

8x-24=0

We move all terms containing x to the left, all other terms to the right

8x=24

x=24/8

x=3

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