Solve by Factoring 16x^2+2x-3=0

Problem

16*x2+2*x−3=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=16 b=2 and c=−3

2. Find two numbers that multiply to a⋅c=16⋅(−3)=−48 and add to b=2 These numbers are 8 and −6

3. Rewrite the middle term 2*x using the two numbers found in the previous step.

16*x2+8*x−6*x−3=0

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

8*x*(2*x+1)−3*(2*x+1)=0

5. Factor out the common binomial (2*x+1)

(8*x−3)*(2*x+1)=0

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

8*x−3=0⇒x=3/8

2*x+1=0⇒x=−1/2

Final Answer

x=3/8,−1/2

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