Z^2-3Z-4=0

Solution for Z^2-3Z-4=0 equation:

Simplifying
Z2 + -3Z + -4 = 0

Reorder the terms:
-4 + -3Z + Z2 = 0

Solving
-4 + -3Z + Z2 = 0

Solving for variable 'Z'.

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

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

Simplifying
-1 + -1Z = 0

Solving
-1 + -1Z = 0

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

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

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

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

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

Simplifying
Z = -1
Subproblem 2
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
Solution
Z = {-1, 4}