Solve by Factoring 3z^2+3z-6=0

Problem

3*z2+3*z−6=0

Solution

1. Factor out the greatest common factor from all terms on the left side of the equation.

3*(z2+z−2)=0

2. Divide both sides by the constant factor to simplify the quadratic expression.

z2+z−2=0

3. Factor the quadratic trinomial by finding two numbers that multiply to −2 and add to 1

(z+2)*(z−1)=0

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

z+2=0

z−1=0

5. Solve for the variable in each linear equation.

z=−2

z=1

Final Answer

z=−2,1

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