(z^2)-2z=24

Solution for (z^2)-2z=24 equation:

Simplifying
(z2) + -2z = 24
z2 + -2z = 24

Reorder the terms:
-2z + z2 = 24

Solving
-2z + z2 = 24

Solving for variable 'z'.

Reorder the terms:
-24 + -2z + z2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -2z + z2 = 0

Factor a trinomial.
(-4 + -1z)(6 + -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 '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-4, 6}