Z^2-57=16Z

Solution for Z^2-57=16Z equation:

Simplifying
Z2 + -57 = 16Z

Reorder the terms:
-57 + Z2 = 16Z

Solving
-57 + Z2 = 16Z

Solving for variable 'Z'.

Reorder the terms:
-57 + -16Z + Z2 = 16Z + -16Z

Combine like terms: 16Z + -16Z = 0
-57 + -16Z + Z2 = 0

Factor a trinomial.
(-3 + -1Z)(19 + -1Z) = 0

Subproblem 1
Set the factor '(-3 + -1Z)' equal to zero and attempt to solve:

Simplifying
-3 + -1Z = 0

Solving
-3 + -1Z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1Z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1Z = 0 + 3
-1Z = 0 + 3

Combine like terms: 0 + 3 = 3
-1Z = 3

Divide each side by '-1'.
Z = -3

Simplifying
Z = -3
Subproblem 2
Set the factor '(19 + -1Z)' equal to zero and attempt to solve:

Simplifying
19 + -1Z = 0

Solving
19 + -1Z = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1Z = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1Z = 0 + -19
-1Z = 0 + -19

Combine like terms: 0 + -19 = -19
-1Z = -19

Divide each side by '-1'.
Z = 19

Simplifying
Z = 19
Solution
Z = {-3, 19}