(z+10)(z-3)=12

Solution for (z+10)(z-3)=12 equation:

Simplifying
(z + 10)(z + -3) = 12

Reorder the terms:
(10 + z)(z + -3) = 12

Reorder the terms:
(10 + z)(-3 + z) = 12

Multiply (10 + z) * (-3 + z)
(10(-3 + z) + z(-3 + z)) = 12
((-3 * 10 + z * 10) + z(-3 + z)) = 12
((-30 + 10z) + z(-3 + z)) = 12
(-30 + 10z + (-3 * z + z * z)) = 12
(-30 + 10z + (-3z + z2)) = 12

Combine like terms: 10z + -3z = 7z
(-30 + 7z + z2) = 12

Solving
-30 + 7z + z2 = 12

Solving for variable 'z'.

Reorder the terms:
-30 + -12 + 7z + z2 = 12 + -12

Combine like terms: -30 + -12 = -42
-42 + 7z + z2 = 12 + -12

Combine like terms: 12 + -12 = 0
-42 + 7z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 7z + 42 + z2 = 0 + 42

Reorder the terms:
-42 + 42 + 7z + z2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 7z + z2 = 0 + 42
7z + z2 = 0 + 42

Combine like terms: 0 + 42 = 42
7z + z2 = 42

The z term is 7z.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7z + 12.25 + z2 = 42 + 12.25

Reorder the terms:
12.25 + 7z + z2 = 42 + 12.25

Combine like terms: 42 + 12.25 = 54.25
12.25 + 7z + z2 = 54.25

Factor a perfect square on the left side:
(z + 3.5)(z + 3.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(z + 3.5) equal to 7.365459931 and -7.365459931.

Subproblem 1
z + 3.5 = 7.365459931

Simplifying
z + 3.5 = 7.365459931

Reorder the terms:
3.5 + z = 7.365459931

Solving
3.5 + z = 7.365459931

Solving for variable 'z'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + z = 7.365459931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + z = 7.365459931 + -3.5
z = 7.365459931 + -3.5

Combine like terms: 7.365459931 + -3.5 = 3.865459931
z = 3.865459931

Simplifying
z = 3.865459931

Subproblem 2
z + 3.5 = -7.365459931

Simplifying
z + 3.5 = -7.365459931

Reorder the terms:
3.5 + z = -7.365459931

Solving
3.5 + z = -7.365459931

Solving for variable 'z'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + z = -7.365459931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + z = -7.365459931 + -3.5
z = -7.365459931 + -3.5

Combine like terms: -7.365459931 + -3.5 = -10.865459931
z = -10.865459931

Simplifying
z = -10.865459931

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {3.865459931, -10.865459931}