(1/2x-3)(x+2)=(5-x)(6-x)

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Solution for (1/2x-3)(x+2)=(5-x)(6-x) equation: 



(1/2x-3)(x+2)=(5-x)(6-x)

We move all terms to the left:

(1/2x-3)(x+2)-((5-x)(6-x))=0



Domain of the equation: 2x-3)(x+2)!=0

x∈R



We add all the numbers together, and all the variables

(1/2x-3)(x+2)-((-1x+5)(-1x+6))=0

We multiply parentheses ..

(+x^2+2x-3x-6)-((-1x+5)(-1x+6))=0



We calculate terms in parentheses: -((-1x+5)(-1x+6)), so:

(-1x+5)(-1x+6)

We multiply parentheses ..

(+x^2-6x-5x+30)

We get rid of parentheses

x^2-6x-5x+30

We add all the numbers together, and all the variables

x^2-11x+30

Back to the equation:

-(x^2-11x+30)



We get rid of parentheses

x^2-x^2+2x-3x+11x-6-30=0

We add all the numbers together, and all the variables

10x-36=0

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

10x=36

x=36/10

x=3+3/5

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