(Z+1)(Z-9)=39

Solution for (Z+1)(Z-9)=39 equation:

Simplifying
(Z + 1)(Z + -9) = 39

Reorder the terms:
(1 + Z)(Z + -9) = 39

Reorder the terms:
(1 + Z)(-9 + Z) = 39

Multiply (1 + Z) * (-9 + Z)
(1(-9 + Z) + Z(-9 + Z)) = 39
((-9 * 1 + Z * 1) + Z(-9 + Z)) = 39
((-9 + 1Z) + Z(-9 + Z)) = 39
(-9 + 1Z + (-9 * Z + Z * Z)) = 39
(-9 + 1Z + (-9Z + Z2)) = 39

Combine like terms: 1Z + -9Z = -8Z
(-9 + -8Z + Z2) = 39

Solving
-9 + -8Z + Z2 = 39

Solving for variable 'Z'.

Reorder the terms:
-9 + -39 + -8Z + Z2 = 39 + -39

Combine like terms: -9 + -39 = -48
-48 + -8Z + Z2 = 39 + -39

Combine like terms: 39 + -39 = 0
-48 + -8Z + Z2 = 0

Factor a trinomial.
(-4 + -1Z)(12 + -1Z) = 0

Subproblem 1
Set the factor '(-4 + -1Z)' equal to zero and attempt to solve:

Simplifying
-4 + -1Z = 0

Solving
-4 + -1Z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1Z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1Z = 0 + 4
-1Z = 0 + 4

Combine like terms: 0 + 4 = 4
-1Z = 4

Divide each side by '-1'.
Z = -4

Simplifying
Z = -4
Subproblem 2
Set the factor '(12 + -1Z)' equal to zero and attempt to solve:

Simplifying
12 + -1Z = 0

Solving
12 + -1Z = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1Z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1Z = 0 + -12
-1Z = 0 + -12

Combine like terms: 0 + -12 = -12
-1Z = -12

Divide each side by '-1'.
Z = 12

Simplifying
Z = 12
Solution
Z = {-4, 12}