10z^2+37z+33=0

Solution for 10z^2+37z+33=0 equation:

Simplifying
10z2 + 37z + 33 = 0

Reorder the terms:
33 + 37z + 10z2 = 0

Solving
33 + 37z + 10z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(11 + 5z)(3 + 2z) = 0

Subproblem 1
Set the factor '(11 + 5z)' equal to zero and attempt to solve:

Simplifying
11 + 5z = 0

Solving
11 + 5z = 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 + 5z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 5z = 0 + -11
5z = 0 + -11

Combine like terms: 0 + -11 = -11
5z = -11

Divide each side by '5'.
z = -2.2

Simplifying
z = -2.2
Subproblem 2
Set the factor '(3 + 2z)' equal to zero and attempt to solve:

Simplifying
3 + 2z = 0

Solving
3 + 2z = 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 + 2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2z = 0 + -3
2z = 0 + -3

Combine like terms: 0 + -3 = -3
2z = -3

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
Solution
z = {-2.2, -1.5}