(z-13)(z+10)=360

Solution for (z-13)(z+10)=360 equation:

Simplifying
(z + -13)(z + 10) = 360

Reorder the terms:
(-13 + z)(z + 10) = 360

Reorder the terms:
(-13 + z)(10 + z) = 360

Multiply (-13 + z) * (10 + z)
(-13(10 + z) + z(10 + z)) = 360
((10 * -13 + z * -13) + z(10 + z)) = 360
((-130 + -13z) + z(10 + z)) = 360
(-130 + -13z + (10 * z + z * z)) = 360
(-130 + -13z + (10z + z2)) = 360

Combine like terms: -13z + 10z = -3z
(-130 + -3z + z2) = 360

Solving
-130 + -3z + z2 = 360

Solving for variable 'z'.

Reorder the terms:
-130 + -360 + -3z + z2 = 360 + -360

Combine like terms: -130 + -360 = -490
-490 + -3z + z2 = 360 + -360

Combine like terms: 360 + -360 = 0
-490 + -3z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '490' to each side of the equation.
-490 + -3z + 490 + z2 = 0 + 490

Reorder the terms:
-490 + 490 + -3z + z2 = 0 + 490

Combine like terms: -490 + 490 = 0
0 + -3z + z2 = 0 + 490
-3z + z2 = 0 + 490

Combine like terms: 0 + 490 = 490
-3z + z2 = 490

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 = 490 + 2.25

Reorder the terms:
2.25 + -3z + z2 = 490 + 2.25

Combine like terms: 490 + 2.25 = 492.25
2.25 + -3z + z2 = 492.25

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = 492.25

Calculate the square root of the right side: 22.186707732

Break this problem into two subproblems by setting 
(z + -1.5) equal to 22.186707732 and -22.186707732.

Subproblem 1
z + -1.5 = 22.186707732

Simplifying
z + -1.5 = 22.186707732

Reorder the terms:
-1.5 + z = 22.186707732

Solving
-1.5 + z = 22.186707732

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 = 22.186707732 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z = 22.186707732 + 1.5
z = 22.186707732 + 1.5

Combine like terms: 22.186707732 + 1.5 = 23.686707732
z = 23.686707732

Simplifying
z = 23.686707732

Subproblem 2
z + -1.5 = -22.186707732

Simplifying
z + -1.5 = -22.186707732

Reorder the terms:
-1.5 + z = -22.186707732

Solving
-1.5 + z = -22.186707732

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 = -22.186707732 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z = -22.186707732 + 1.5
z = -22.186707732 + 1.5

Combine like terms: -22.186707732 + 1.5 = -20.686707732
z = -20.686707732

Simplifying
z = -20.686707732

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {23.686707732, -20.686707732}