First, solve for \( \left|z + 4\right| \):

\( \left|z + 4\right| \) + 4 = -5
\( \left|z + 4\right| \) = -5 - 4
\( \left|z + 4\right| \) = -9

The value inside the absolute value brackets can be either positive or negative so (z + 4) must equal - 9 or --9 for \( \left|z + 4\right| \) to equal -9:

So, z = 5 or z = -13.

The equation for this sequence is:

a_n = a_n-1 + 7

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 7
a₆ = 29 + 7
a₆ = 36

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-3c⁶ x 6c⁴
(-3 x 6)c^{(6 + 4)}
-18c¹⁰

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).