z^2+4z=5

Solution for z^2+4z=5 equation:

Simplifying
z2 + 4z = 5

Reorder the terms:
4z + z2 = 5

Solving
4z + z2 = 5

Solving for variable 'z'.

Reorder the terms:
-5 + 4z + z2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 4z + z2 = 0

Factor a trinomial.
(-5 + -1z)(1 + -1z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
z = {-5, 1}