Solve by Factoring 2m^2-m-15=0

Problem

2*m2−m−15=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*m2+b*m+c=0 where a=2 b=−1 and c=−15

2. Find two numbers that multiply to a⋅c=2⋅(−15)=−30 and add to b=−1 These numbers are −6 and 5

3. Rewrite the middle term −m using the two numbers found in the previous step.

2*m2−6*m+5*m−15=0

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

2*m*(m−3)+5*(m−3)=0

5. Factor out the common binomial (m−3)

(2*m+5)*(m−3)=0

6. Apply the zero product property by setting each factor equal to zero and solving for m

2*m+5=0⇒m=−5/2

m−3=0⇒m=3

Final Answer

m=−5/2,3

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