-z^2+4z=4

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

Simplifying
-1z2 + 4z = 4

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

Solving
4z + -1z2 = 4

Solving for variable 'z'.

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

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

Factor a trinomial.
(-2 + z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-2 + z)' equal to zero and attempt to solve:

Simplifying
-2 + z = 0

Solving
-2 + z = 0

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

Add '2' to each side of the equation.
-2 + 2 + z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + z = 0 + 2
z = 0 + 2

Combine like terms: 0 + 2 = 2
z = 2

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {2, 2}