48=z^2+8z

Solution for 48=z^2+8z equation:

Simplifying
48 = z2 + 8z

Reorder the terms:
48 = 8z + z2

Solving
48 = 8z + z2

Solving for variable 'z'.

Reorder the terms:
48 + -8z + -1z2 = 8z + -8z + z2 + -1z2

Combine like terms: 8z + -8z = 0
48 + -8z + -1z2 = 0 + z2 + -1z2
48 + -8z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
48 + -8z + -1z2 = 0

Factor a trinomial.
(4 + -1z)(12 + z) = 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 '(12 + z)' equal to zero and attempt to solve:

Simplifying
12 + z = 0

Solving
12 + z = 0

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

Add '-12' to each side of the equation.
12 + -12 + z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + z = 0 + -12
z = 0 + -12

Combine like terms: 0 + -12 = -12
z = -12

Simplifying
z = -12
Solution
z = {4, -12}