6z=-z^2-9

Solution for 6z=-z^2-9 equation:

Simplifying
6z = -1z2 + -9

Reorder the terms:
6z = -9 + -1z2

Solving
6z = -9 + -1z2

Solving for variable 'z'.

Reorder the terms:
9 + 6z + z2 = -9 + -1z2 + 9 + z2

Reorder the terms:
9 + 6z + z2 = -9 + 9 + -1z2 + z2

Combine like terms: -9 + 9 = 0
9 + 6z + z2 = 0 + -1z2 + z2
9 + 6z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
9 + 6z + z2 = 0

Factor a trinomial.
(3 + z)(3 + z) = 0

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

Simplifying
3 + z = 0

Solving
3 + z = 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 + z = 0 + -3

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

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

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

Simplifying
3 + z = 0

Solving
3 + z = 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 + z = 0 + -3

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

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

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