SOLUTION: Use factoring to solve the equation 6x^2+23x-18=0

Algebra ->  Equations -> SOLUTION: Use factoring to solve the equation 6x^2+23x-18=0      Log On


   



Question 442599: Use factoring to solve the equation
6x^2+23x-18=0

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the trick:
Take the a term and multiply it by the c term. 6 * -18 = -108. List the factors of -108.
plus or minus
--------------
1 108
2 54
3 36
4 27
6 18
9 12
Is there any way to get -23 out of this?
yes, 4 - 27 gives us -23.
Thus we will have a 4x term and a -27x term.
so we can rewrite this as 6x%5E2+%2B+4x+-+27x+-18
Group the first two terms and last two terms and factor out the common factor.
2x%283x%2B2%29+-+9%283x%2B2%29++=+%282x-9%29%283x%2B2%29
Thus our factorization is %282x-9%29%283x%2B2%29
Set each factor equal to 0:
(2x-9) = 0 ---> 2x = 9 x =9/2
(3x+2) = 0 ---> 3x = -2 x = -2/3
So our two solutions are x=expr%289%2F2%29x=expr%28-2%2F3%29