how to factor these problems then solve the problems step by step

Question

x²-6x=-8

And 

x²+1x+12=0

And

x²+7x+12=0

Answer 1

x² - 6x = 8

 

Set equal to 0:  x² - 6x + 8 = 0

 

What factors of 8 add to be 6?  Try 4, and 2.

 

Note:  The 8 is positive, therefore both signs will be the same as the middle term.  i.e. negative.

 

Therefore:  x² - 6x + 8 = 0, becomes (x - 4)(x - 2) = 0.  Use the zero products rule and set each factor equal to 0.

 

x - 4 = 0,    x - 2 = 0

x = 4           x = 2

 

x² + x + 12 does not factor.  Do you mean x² - x - 12?  If so, find 2 factors of 12 whose difference is 1 and make the larger one negative:

 x² - x - 12 = (x - 4)(x + 3) = 0.  Therefore, the answers are x = 4, and x = -3.

 

x² + 7x + 12 = 0.  Find 2 factors of 12 whose sum is 7.

 

x² + 7x + 12 = (x + 4)(x + 3) = 0.  Therefore, x = -4, and x = -3.

 

I hope this helps.