2z-9=-5-z(2z+8)

Solution for 2z-9=-5-z(2z+8) equation:

Simplifying
2z + -9 = -5 + -1z(2z + 8)

Reorder the terms:
-9 + 2z = -5 + -1z(2z + 8)

Reorder the terms:
-9 + 2z = -5 + -1z(8 + 2z)
-9 + 2z = -5 + (8 * -1z + 2z * -1z)
-9 + 2z = -5 + (-8z + -2z2)

Solving
-9 + 2z = -5 + -8z + -2z2

Solving for variable 'z'.

Reorder the terms:
-9 + 5 + 2z + 8z + 2z2 = -5 + -8z + -2z2 + 5 + 8z + 2z2

Combine like terms: -9 + 5 = -4
-4 + 2z + 8z + 2z2 = -5 + -8z + -2z2 + 5 + 8z + 2z2

Combine like terms: 2z + 8z = 10z
-4 + 10z + 2z2 = -5 + -8z + -2z2 + 5 + 8z + 2z2

Reorder the terms:
-4 + 10z + 2z2 = -5 + 5 + -8z + 8z + -2z2 + 2z2

Combine like terms: -5 + 5 = 0
-4 + 10z + 2z2 = 0 + -8z + 8z + -2z2 + 2z2
-4 + 10z + 2z2 = -8z + 8z + -2z2 + 2z2

Combine like terms: -8z + 8z = 0
-4 + 10z + 2z2 = 0 + -2z2 + 2z2
-4 + 10z + 2z2 = -2z2 + 2z2

Combine like terms: -2z2 + 2z2 = 0
-4 + 10z + 2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5z + z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + 5z + z2)' equal to zero and attempt to solve:

Simplifying
-2 + 5z + z2 = 0

Solving
-2 + 5z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 5z + 2 + z2 = 0 + 2

Reorder the terms:
-2 + 2 + 5z + z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5z + z2 = 0 + 2
5z + z2 = 0 + 2

Combine like terms: 0 + 2 = 2
5z + z2 = 2

The z term is 5z.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5z + 6.25 + z2 = 2 + 6.25

Reorder the terms:
6.25 + 5z + z2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + 5z + z2 = 8.25

Factor a perfect square on the left side:
(z + 2.5)(z + 2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(z + 2.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
z + 2.5 = 2.872281323

Simplifying
z + 2.5 = 2.872281323

Reorder the terms:
2.5 + z = 2.872281323

Solving
2.5 + z = 2.872281323

Solving for variable 'z'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + z = 2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + z = 2.872281323 + -2.5
z = 2.872281323 + -2.5

Combine like terms: 2.872281323 + -2.5 = 0.372281323
z = 0.372281323

Simplifying
z = 0.372281323

Subproblem 2
z + 2.5 = -2.872281323

Simplifying
z + 2.5 = -2.872281323

Reorder the terms:
2.5 + z = -2.872281323

Solving
2.5 + z = -2.872281323

Solving for variable 'z'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + z = -2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + z = -2.872281323 + -2.5
z = -2.872281323 + -2.5

Combine like terms: -2.872281323 + -2.5 = -5.372281323
z = -5.372281323

Simplifying
z = -5.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.372281323, -5.372281323}
Solution
z = {0.372281323, -5.372281323}