6z^2+31z+5=0

Solution for 6z^2+31z+5=0 equation:

Simplifying
6z2 + 31z + 5 = 0

Reorder the terms:
5 + 31z + 6z2 = 0

Solving
5 + 31z + 6z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + z)(1 + 6z) = 0

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

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

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

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

Simplifying
z = -5
Subproblem 2
Set the factor '(1 + 6z)' equal to zero and attempt to solve:

Simplifying
1 + 6z = 0

Solving
1 + 6z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 6z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6z = 0 + -1
6z = 0 + -1

Combine like terms: 0 + -1 = -1
6z = -1

Divide each side by '6'.
z = -0.1666666667

Simplifying
z = -0.1666666667
Solution
z = {-5, -0.1666666667}