2e^2+e-3=0

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

Simplifying
2e2 + e + -3 = 0

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

Solving
-3 + e + 2e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(-3 + -2e)(1 + -1e) = 0

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

Simplifying
-3 + -2e = 0

Solving
-3 + -2e = 0

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

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

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

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

Divide each side by '-2'.
e = -1.5

Simplifying
e = -1.5
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 = {-1.5, 1}