Factor 6n^2+5n-6

Problem

6*n2+5*n−6

Solution

1. Identify the coefficients of the quadratic expression a*n2+b*n+c where a=6 b=5 and c=−6

2. Calculate the product a*c which is 6×−6=−36

3. Find two numbers that multiply to −36 and add to the middle coefficient b=5 These numbers are 9 and −4

4. Rewrite the middle term 5*n using the two numbers found: 9*n−4*n

6*n2+9*n−4*n−6

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*n*(2*n+3)−2*(2*n+3)

6. Factor out the common binomial (2*n+3)

(3*n−2)*(2*n+3)

Final Answer

6*n2+5*n−6=(3*n−2)*(2*n+3)

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