3e^2-2e-1=0

Solution for 3e^2-2e-1=0 equation:

Simplifying
3e2 + -2e + -1 = 0

Reorder the terms:
-1 + -2e + 3e2 = 0

Solving
-1 + -2e + 3e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(-1 + -3e)(1 + -1e) = 0

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

Simplifying
-1 + -3e = 0

Solving
-1 + -3e = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3e = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3e = 0 + 1
-3e = 0 + 1

Combine like terms: 0 + 1 = 1
-3e = 1

Divide each side by '-3'.
e = -0.3333333333

Simplifying
e = -0.3333333333
Subproblem 2
Set the factor '(1 + -1e)' equal to zero and attempt to solve:

Simplifying
1 + -1e = 0

Solving
1 + -1e = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1e = 0 + -1
-1e = 0 + -1

Combine like terms: 0 + -1 = -1
-1e = -1

Divide each side by '-1'.
e = 1

Simplifying
e = 1
Solution
e = {-0.3333333333, 1}