Find the number ab, when (a+b-3)-6a=-a^2-9.
-7a=-9-b or 7a=9+b
then you do this
If we are moving the terms from the right side to the left side of the equality and if we are grouping them with the term "-6a", the result will be:
(a+b-3) + (-6a+a^2+9)=0
The new group (-6a+a^2+9) could be written as (a-3)^2.
(a+b-3) + (a-3)^2=0
The condition of equivalence between 2 expressions is that the equivalent terms from both expressions to be equal.
(a+b-3)=0 and (a-3)^2=0
From (a-3)^2=0 it results that a-3=0, so a=3
By substituting the value of a into the relation (a+b-3)=0, this one will become:
3+b-3=0, so b=0.
From both relations it results that the number ab=30.