z(z+5)=24

Solution for z(z+5)=24 equation:

Simplifying
z(z + 5) = 24

Reorder the terms:
z(5 + z) = 24
(5 * z + z * z) = 24
(5z + z2) = 24

Solving
5z + z2 = 24

Solving for variable 'z'.

Reorder the terms:
-24 + 5z + z2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 5z + z2 = 0

Factor a trinomial.
(-8 + -1z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-8 + -1z)' equal to zero and attempt to solve:

Simplifying
-8 + -1z = 0

Solving
-8 + -1z = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1z = 0 + 8
-1z = 0 + 8

Combine like terms: 0 + 8 = 8
-1z = 8

Divide each side by '-1'.
z = -8

Simplifying
z = -8
Subproblem 2
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
Solution
z = {-8, 3}