6z(2z+1)+2z+1=

Solution for 6z(2z+1)+2z+1= equation:

Simplifying
6z(2z + 1) + 2z + 1 = 0

Reorder the terms:
6z(1 + 2z) + 2z + 1 = 0
(1 * 6z + 2z * 6z) + 2z + 1 = 0
(6z + 12z2) + 2z + 1 = 0

Reorder the terms:
1 + 6z + 2z + 12z2 = 0

Combine like terms: 6z + 2z = 8z
1 + 8z + 12z2 = 0

Solving
1 + 8z + 12z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
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 = {-0.5, -0.1666666667}