12z^2+11z+2=0

Solution for 12z^2+11z+2=0 equation:

Simplifying
12z2 + 11z + 2 = 0

Reorder the terms:
2 + 11z + 12z2 = 0

Solving
2 + 11z + 12z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + 3z)(1 + 4z) = 0

Subproblem 1
Set the factor '(2 + 3z)' equal to zero and attempt to solve:

Simplifying
2 + 3z = 0

Solving
2 + 3z = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3z = 0 + -2

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

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

Divide each side by '3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Subproblem 2
Set the factor '(1 + 4z)' equal to zero and attempt to solve:

Simplifying
1 + 4z = 0

Solving
1 + 4z = 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 + 4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4z = 0 + -1
4z = 0 + -1

Combine like terms: 0 + -1 = -1
4z = -1

Divide each side by '4'.
z = -0.25

Simplifying
z = -0.25
Solution
z = {-0.6666666667, -0.25}