(y-2)(y+3)=6

Question

(y-2)(y+3)=6

anonymous · Answer

y= -4,3

anonymous · Answer

how did you get that?

parthkohli · Answer

Ever heard of the zero-product rule?

anonymous · Answer

no

parthkohli · Answer

$$(x + a)(x + b) = 0 \implies x = -a \text{ or }-b $$

parthkohli · Answer

Not to think too hard about it. It's just based on how product of two numbers is zero if one number is 0.

parthkohli · Answer

Basically,$$x y = 0 \implies x = 0 \text{ or }y = 0$$

anonymous · Answer

(y · y+y · 3-2 · y-2 · 3)=6 

y^2-y+y-6=6

y^2+y-12=0

use ZPP

(y+4)(y-3)=0

y=4  
y=-3

anonymous · Answer

ok thanks!

mathmate · Answer

We can expand the left-hand side and regroup and re-factor the left-hand side, as is done above.
For this particular problem, we can do it mentally in a wicked way:
(y-2)(y+3)=6
We can, "slide" the numerical factor upwards or downwards, thereby keeping the difference equal to +1 as follows:
Given (y-2)(y+3)=6
(y-3)(y+4)+(-2)(3)-(-3)(4)=6  [think 3*4-2*3=6]
(y-3)(y+4)+6=6
(y-3)(y+4)=0
So the answer is 3, -4
@mitchelsewbaran the last two lines should read 3, -4