A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

-6c + 8z = -7c - 4z - 5
-6c = -7c - 4z - 5 - 8z
-6c + 7c = -4z - 5 - 8z
c = -12z - 5

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 + z + 4 = 4z + 2
z² + z + 4 - 2 = 4z
z² + z - 4z + 2 = 0
z² - 3z + 2 = 0

Next, factor the quadratic equation:

z² - 3z + 2 = 0
(z - 1)(z - 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 1) or (z - 2) must equal zero:

If (z - 1) = 0, z must equal 1
If (z - 2) = 0, z must equal 2

So the solution is that z = 1 or 2

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

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

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

z² - 1 = 0
(z - 1)(z + 1) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 1) or (z + 1) must equal zero:

If (z - 1) = 0, z must equal 1
If (z + 1) = 0, z must equal -1

So the solution is that z = 1 or -1