Alg3.6.3

From Exampleproblems

Solve for $x: 5x^2-12x+7=0\,$

Multiplying the coefficient of $x^2\,$ and the constant gives $35\,$ . The different factors for $35\,$ are $(7,5)(-7,-5)\,$ .

The combination which suits the coefficient of -12 is $(-7,-5)\,$ .

Now splitting the x coefficient,the equation looks like $5x^2-5x-7x+7=0\,$

Taking out the common terms in the first two and the last two terms $5x(x-1)-7(x-1)=0\,$

Taking out the common terms in the above $(5x-7)(x-1)=0\,$

Final solution is $(5x-7)=0\,$ or $(x-1)=0\,$

$x=7/5\,$ or $x=1\,$