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

z² + 13z + 42 = 0
(z + 6)(z + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 6) or (z + 7) must equal zero:

If (z + 6) = 0, z must equal -6
If (z + 7) = 0, z must equal -7

So the solution is that z = -6 or -7

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).

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(6a)(8ab) - (9a²)(8b)
(6 x 8)(a x a x b) - (9 x 8)(a² x b)
(48)(a¹⁺¹ x b) - (72)(a²b)
48a²b - 72a²b
-24a²b

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(5 + 2)(5)
a = ½(7)(5)
a = ½(35) = \( \frac{35}{2} \)
a = 17\(\frac{1}{2}\)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².