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 - 2z - 14 = 2z - 2
z² - 2z - 14 + 2 = 2z
z² - 2z - 2z - 12 = 0
z² - 4z - 12 = 0

Next, factor the quadratic equation:

z² - 4z - 12 = 0
(z + 2)(z - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 2) or (z - 6) must equal zero:

If (z + 2) = 0, z must equal -2
If (z - 6) = 0, z must equal 6

So the solution is that z = -2 or 6

The volume of a cylinder is πr²h:

v = πr²h
v = π(3² x 8)
v = 72π

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 7 + 6 + 2 + 9
p = 24

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 -72 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -8 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 72
y² + (-8 + 9)y + (-8 x 9)
(y - 8)(y + 9)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).