z^2-14z-72=0

Solution for z^2-14z-72=0 equation:

Simplifying
z2 + -14z + -72 = 0

Reorder the terms:
-72 + -14z + z2 = 0

Solving
-72 + -14z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z)(18 + -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 '(18 + -1z)' equal to zero and attempt to solve:

Simplifying
18 + -1z = 0

Solving
18 + -1z = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1z = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1z = 0 + -18
-1z = 0 + -18

Combine like terms: 0 + -18 = -18
-1z = -18

Divide each side by '-1'.
z = 18

Simplifying
z = 18
Solution
z = {-4, 18}