z^2+2z-224=0

Solution for z^2+2z-224=0 equation:

Simplifying
z2 + 2z + -224 = 0

Reorder the terms:
-224 + 2z + z2 = 0

Solving
-224 + 2z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-16 + -1z)(14 + -1z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(14 + -1z)' equal to zero and attempt to solve:

Simplifying
14 + -1z = 0

Solving
14 + -1z = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1z = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1z = 0 + -14
-1z = 0 + -14

Combine like terms: 0 + -14 = -14
-1z = -14

Divide each side by '-1'.
z = 14

Simplifying
z = 14
Solution
z = {-16, 14}