Solve by Factoring z^2+2z-15=0

Problem

z2+2*z−15=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*z2+b*z+c=0 where a=1 b=2 and c=−15

2. Find two numbers that multiply to c (−15 and add to b (2.

3. Determine that the numbers are 5 and −3 because 5⋅(−3)=−15 and 5 + (-3) = 2$.

4. Rewrite the quadratic expression as a product of two binomials using these numbers.

(z+5)*(z−3)=0

5. Apply the zero product property by setting each factor equal to zero.

z+5=0

z−3=0

6. Solve each linear equation for z

z=−5

z=3

Final Answer

z=−5,3

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