When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

z² + 9z + 7 = 3z - 1
z² + 9z + 7 + 1 = 3z
z² + 9z - 3z + 8 = 0
z² + 6z + 8 = 0

Next, factor the quadratic equation:

z² + 6z + 8 = 0
(z + 2)(z + 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 2) or (z + 4) must equal zero:

If (z + 2) = 0, z must equal -2
If (z + 4) = 0, z must equal -4

So the solution is that z = -2 or -4

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(1²) + 2π(1 x 4)
sa = 2π(1) + 2π(4)
sa = (2 x 1)π + (2 x 4)π
sa = 2π + 8π
sa = 10π

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -4 as well and sum (Inside, Outside) to equal 0. For this problem, those two numbers are -2 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 4
y² + (-2 + 2)y + (-2 x 2)
(y - 2)(y + 2)