z^2-4z=-24+6z

Solution for z^2-4z=-24+6z equation:

Simplifying
z2 + -4z = -24 + 6z

Reorder the terms:
-4z + z2 = -24 + 6z

Solving
-4z + z2 = -24 + 6z

Solving for variable 'z'.

Reorder the terms:
24 + -4z + -6z + z2 = -24 + 6z + 24 + -6z

Combine like terms: -4z + -6z = -10z
24 + -10z + z2 = -24 + 6z + 24 + -6z

Reorder the terms:
24 + -10z + z2 = -24 + 24 + 6z + -6z

Combine like terms: -24 + 24 = 0
24 + -10z + z2 = 0 + 6z + -6z
24 + -10z + z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
24 + -10z + 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}