6z^2+z-2=0

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

Simplifying
6z2 + z + -2 = 0

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

Solving
-2 + z + 6z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -3z)(1 + -2z) = 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 + -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 = {-0.6666666667, 0.5}