z^2-5z=33+3z

Solution for z^2-5z=33+3z equation:

Simplifying
z2 + -5z = 33 + 3z

Reorder the terms:
-5z + z2 = 33 + 3z

Solving
-5z + z2 = 33 + 3z

Solving for variable 'z'.

Reorder the terms:
-33 + -5z + -3z + z2 = 33 + 3z + -33 + -3z

Combine like terms: -5z + -3z = -8z
-33 + -8z + z2 = 33 + 3z + -33 + -3z

Reorder the terms:
-33 + -8z + z2 = 33 + -33 + 3z + -3z

Combine like terms: 33 + -33 = 0
-33 + -8z + z2 = 0 + 3z + -3z
-33 + -8z + z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
-33 + -8z + z2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
z = {-3, 11}