Question

Solve the equation by factoring. 3z² 3z − 6 = 0 z = 1 or z = 2 z = 3 or z = 2 z = 3 or z = –2 z = 1 or z = –2

Answer 1

To solve the given equation by factoring, we can rewrite it in quadratic form and then factor out the expression. Finally, we set each factor equal to zero and solve for z.

Step-by-step explanation:

To solve the equation by factoring, we need to rewrite it in quadratic form: 3z² + 3z - 6 = 0.

Next, we can factor out a common factor of 3: 3(z² + z - 2) = 0.

Then we factor the quadratic expression inside the parentheses: 3(z - 1)(z + 2) = 0.

Finally, we set each factor equal to zero and solve for z: z - 1 = 0 or z + 2 = 0. This gives us the solutions z = 1 or z = -2.