Take for example, the equation
13a + 6a2 = −6
rearrange the questions into the form ax2+bx+c=0
6a2 + 13a + 6 = 0
method 1: cross-multiplication method
you use the cross multiplication method to find the common factors
3 2
2 3
____________________
3×2=6 2×3=6
(you get 6a2) (you get 6)
imagine a cross in the middle
3×3+2×2=13 (you reach the middle number 13a)
so you know this set of numbers are correct, so you can come to the answer
(3a+2) (2a+3)=0
JUST TO CHECK THAT YOU HAVE GOT A CORRECT ANSWER
you can check your work by expanding the brackets
like this
(3a+2)(2a+3)
=3a(2a+3)+2(2a+3)
=6a2+9a+4a+6 (simplify)
=6a2+13a+6 (same as the original question, so you know you have factorized it right)
àsolve the problem
3a+2=0 or 2a+3=0
a= −⅔ or −3/2
method 2: quadratic formula
if you find the cross-multiplication method too complicated, you can use the quadratic formula
6a2 + 13a + 6 = 0
−b ± √(b2 − 4ac)
answers= _____________________
2a
in this case,
a=6
b=13
c=6
(derived from the arranged form of the equation given)
substitute these numbers into the formula
answers
= (−13)+√(132−4(6)(6)) ÷2(6) or = (−13)+√(132−4(6)(6)) ÷2(6)
= −⅔ or −3/2
for both methods, you get the same solutions