z^2+8z-33=0

Solution for z^2+8z-33=0 equation:

Simplifying
z2 + 8z + -33 = 0

Reorder the terms:
-33 + 8z + z2 = 0

Solving
-33 + 8z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-11 + -1z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-11 + -1z)' equal to zero and attempt to solve:

Simplifying
-11 + -1z = 0

Solving
-11 + -1z = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1z = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1z = 0 + 11
-1z = 0 + 11

Combine like terms: 0 + 11 = 11
-1z = 11

Divide each side by '-1'.
z = -11

Simplifying
z = -11
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-11, 3}