6z^2-37z-553=0

Solution for 6z^2-37z-553=0 equation:

Simplifying
6z2 + -37z + -553 = 0

Reorder the terms:
-553 + -37z + 6z2 = 0

Solving
-553 + -37z + 6z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z)(79 + -6z) = 0

Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
Subproblem 2
Set the factor '(79 + -6z)' equal to zero and attempt to solve:

Simplifying
79 + -6z = 0

Solving
79 + -6z = 0

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

Add '-79' to each side of the equation.
79 + -79 + -6z = 0 + -79

Combine like terms: 79 + -79 = 0
0 + -6z = 0 + -79
-6z = 0 + -79

Combine like terms: 0 + -79 = -79
-6z = -79

Divide each side by '-6'.
z = 13.16666667

Simplifying
z = 13.16666667
Solution
z = {-7, 13.16666667}