z^2-32=14z

Solution for z^2-32=14z equation:

Simplifying
z2 + -32 = 14z

Reorder the terms:
-32 + z2 = 14z

Solving
-32 + z2 = 14z

Solving for variable 'z'.

Reorder the terms:
-32 + -14z + z2 = 14z + -14z

Combine like terms: 14z + -14z = 0
-32 + -14z + z2 = 0

Factor a trinomial.
(-2 + -1z)(16 + -1z) = 0

Subproblem 1
Set the factor '(-2 + -1z)' equal to zero and attempt to solve:

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
Set the factor '(16 + -1z)' equal to zero and attempt to solve:

Simplifying
16 + -1z = 0

Solving
16 + -1z = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1z = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1z = 0 + -16
-1z = 0 + -16

Combine like terms: 0 + -16 = -16
-1z = -16

Divide each side by '-1'.
z = 16

Simplifying
z = 16
Solution
z = {-2, 16}