3e(3e-1)=2

Solution for 3e(3e-1)=2 equation:

Simplifying
3e(3e + -1) = 2

Reorder the terms:
3e(-1 + 3e) = 2
(-1 * 3e + 3e * 3e) = 2
(-3e + 9e2) = 2

Solving
-3e + 9e2 = 2

Solving for variable 'e'.

Reorder the terms:
-2 + -3e + 9e2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -3e + 9e2 = 0

Factor a trinomial.
(-1 + -3e)(2 + -3e) = 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 '(2 + -3e)' equal to zero and attempt to solve:

Simplifying
2 + -3e = 0

Solving
2 + -3e = 0

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

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

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

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

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

Simplifying
e = 0.6666666667
Solution
e = {-0.3333333333, 0.6666666667}