Solve by Factoring 9x^2+21x-8=0

Problem

9*x2+21*x−8=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=9 b=21 and c=−8

2. Find two numbers that multiply to a*c=9⋅(−8)=−72 and add to b=21 These numbers are 24 and −3

3. Rewrite the middle term 21*x using the two numbers found: 24*x−3*x

9*x2+24*x−3*x−8=0

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

3*x*(3*x+8)−1*(3*x+8)=0

5. Factor out the common binomial (3*x+8)

(3*x+8)*(3*x−1)=0

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

3*x+8=0⇒x=−8/3

3*x−1=0⇒x=1/3

Final Answer

x=−8/3,1/3

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