2e^2+3e=27

Solution for 2e^2+3e=27 equation:

Simplifying
2e2 + 3e = 27

Reorder the terms:
3e + 2e2 = 27

Solving
3e + 2e2 = 27

Solving for variable 'e'.

Reorder the terms:
-27 + 3e + 2e2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 3e + 2e2 = 0

Factor a trinomial.
(-9 + -2e)(3 + -1e) = 0

Subproblem 1
Set the factor '(-9 + -2e)' equal to zero and attempt to solve:

Simplifying
-9 + -2e = 0

Solving
-9 + -2e = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2e = 0 + 9

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

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

Divide each side by '-2'.
e = -4.5

Simplifying
e = -4.5
Subproblem 2
Set the factor '(3 + -1e)' equal to zero and attempt to solve:

Simplifying
3 + -1e = 0

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

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

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

Divide each side by '-1'.
e = 3

Simplifying
e = 3
Solution
e = {-4.5, 3}