z(z-2)=48

Solution for z(z-2)=48 equation:

Simplifying
z(z + -2) = 48

Reorder the terms:
z(-2 + z) = 48
(-2 * z + z * z) = 48
(-2z + z2) = 48

Solving
-2z + z2 = 48

Solving for variable 'z'.

Reorder the terms:
-48 + -2z + z2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -2z + z2 = 0

Factor a trinomial.
(-6 + -1z)(8 + -1z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
z = {-6, 8}