z^2-16=z+4

Solution for z^2-16=z+4 equation:

Simplifying
z2 + -16 = z + 4

Reorder the terms:
-16 + z2 = z + 4

Reorder the terms:
-16 + z2 = 4 + z

Solving
-16 + z2 = 4 + z

Solving for variable 'z'.

Reorder the terms:
-16 + -4 + -1z + z2 = 4 + z + -4 + -1z

Combine like terms: -16 + -4 = -20
-20 + -1z + z2 = 4 + z + -4 + -1z

Reorder the terms:
-20 + -1z + z2 = 4 + -4 + z + -1z

Combine like terms: 4 + -4 = 0
-20 + -1z + z2 = 0 + z + -1z
-20 + -1z + z2 = z + -1z

Combine like terms: z + -1z = 0
-20 + -1z + z2 = 0

Factor a trinomial.
(-4 + -1z)(5 + -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 '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {-4, 5}