(z^2+9)-5(3+z)=18

Solution for (z^2+9)-5(3+z)=18 equation:

Simplifying
(z2 + 9) + -5(3 + z) = 18

Reorder the terms:
(9 + z2) + -5(3 + z) = 18

Remove parenthesis around (9 + z2)
9 + z2 + -5(3 + z) = 18
9 + z2 + (3 * -5 + z * -5) = 18
9 + z2 + (-15 + -5z) = 18

Reorder the terms:
9 + -15 + -5z + z2 = 18

Combine like terms: 9 + -15 = -6
-6 + -5z + z2 = 18

Solving
-6 + -5z + z2 = 18

Solving for variable 'z'.

Reorder the terms:
-6 + -18 + -5z + z2 = 18 + -18

Combine like terms: -6 + -18 = -24
-24 + -5z + z2 = 18 + -18

Combine like terms: 18 + -18 = 0
-24 + -5z + z2 = 0

Factor a trinomial.
(-3 + -1z)(8 + -1z) = 0

Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
z = 8

Simplifying
z = 8
Solution
z = {-3, 8}