Solve by Factoring z^2-6z-27=0

Problem

z2−6*z−27=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*z2+b*z+c=0 where a=1 b=−6 and c=−27

2. Find two numbers that multiply to c (−27 and add to b (−6.

3. Determine the factors by testing pairs: −9 and 3 satisfy the conditions because (−9)×3=−27 and −9+3=−6

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

(z−9)*(z+3)=0

5. Apply the Zero Product Property by setting each factor equal to zero.

z−9=0

z+3=0

6. Solve each linear equation for z

z=9

z=−3

Final Answer

z2−6*z−27=0⇒z=9,−3

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