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

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

Simplifying
(z + 5)(z + -2) = -5

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

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

Multiply (5 + z) * (-2 + z)
(5(-2 + z) + z(-2 + z)) = -5
((-2 * 5 + z * 5) + z(-2 + z)) = -5
((-10 + 5z) + z(-2 + z)) = -5
(-10 + 5z + (-2 * z + z * z)) = -5
(-10 + 5z + (-2z + z2)) = -5

Combine like terms: 5z + -2z = 3z
(-10 + 3z + z2) = -5

Solving
-10 + 3z + z2 = -5

Solving for variable 'z'.

Reorder the terms:
-10 + 5 + 3z + z2 = -5 + 5

Combine like terms: -10 + 5 = -5
-5 + 3z + z2 = -5 + 5

Combine like terms: -5 + 5 = 0
-5 + 3z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3z + 5 + z2 = 0 + 5

Reorder the terms:
-5 + 5 + 3z + z2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3z + z2 = 0 + 5
3z + z2 = 0 + 5

Combine like terms: 0 + 5 = 5
3z + z2 = 5

The z term is 3z.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3z + 2.25 + z2 = 5 + 2.25

Reorder the terms:
2.25 + 3z + z2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + 3z + z2 = 7.25

Factor a perfect square on the left side:
(z + 1.5)(z + 1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(z + 1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
z + 1.5 = 2.692582404

Simplifying
z + 1.5 = 2.692582404

Reorder the terms:
1.5 + z = 2.692582404

Solving
1.5 + z = 2.692582404

Solving for variable 'z'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + z = 2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + z = 2.692582404 + -1.5
z = 2.692582404 + -1.5

Combine like terms: 2.692582404 + -1.5 = 1.192582404
z = 1.192582404

Simplifying
z = 1.192582404

Subproblem 2
z + 1.5 = -2.692582404

Simplifying
z + 1.5 = -2.692582404

Reorder the terms:
1.5 + z = -2.692582404

Solving
1.5 + z = -2.692582404

Solving for variable 'z'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + z = -2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + z = -2.692582404 + -1.5
z = -2.692582404 + -1.5

Combine like terms: -2.692582404 + -1.5 = -4.192582404
z = -4.192582404

Simplifying
z = -4.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.192582404, -4.192582404}