2z^2+13z+6=0

Solution for 2z^2+13z+6=0 equation:

Simplifying
2z2 + 13z + 6 = 0

Reorder the terms:
6 + 13z + 2z2 = 0

Solving
6 + 13z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + z)(1 + 2z) = 0

Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

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

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

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

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

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

Simplifying
1 + 2z = 0

Solving
1 + 2z = 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 + 2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z = 0 + -1
2z = 0 + -1

Combine like terms: 0 + -1 = -1
2z = -1

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {-6, -0.5}