Final answer:
To solve the equation, collect like terms and set the equation equal to zero. Factor the quadratic equation and solve for z to find the solutions.
Step-by-step explanation:
To solve the equation, we need to collect like terms and then set the equation equal to zero. This can be done by subtracting the right side of the equation from the left side:
6z² + 27z + 47 - (5z² + 42z - 7) = 0
Simplify the equation:
6z² + 27z + 47 - 5z² - 42z + 7 = 0
Combine like terms:
z² - 15z + 54 = 0
This quadratic equation can be factored as:
(z - 6)(z - 9) = 0
Set each factor equal to zero and solve for z:
z - 6 = 0, z - 9 = 0
z = 6, z = 9
The solutions to the equation are z = 6 and z = 9.