-z^2+6=-5z

Solution for -z^2+6=-5z equation:

Simplifying
-1z2 + 6 = -5z

Reorder the terms:
6 + -1z2 = -5z

Solving
6 + -1z2 = -5z

Solving for variable 'z'.

Reorder the terms:
6 + 5z + -1z2 = -5z + 5z

Combine like terms: -5z + 5z = 0
6 + 5z + -1z2 = 0

Factor a trinomial.
(6 + -1z)(1 + z) = 0

Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

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

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

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

Simplifying
z = -1
Solution
z = {6, -1}