3e^2+5=-8e

Solution for 3e^2+5=-8e equation:

Simplifying
3e2 + 5 = -8e

Reorder the terms:
5 + 3e2 = -8e

Solving
5 + 3e2 = -8e

Solving for variable 'e'.

Reorder the terms:
5 + 8e + 3e2 = -8e + 8e

Combine like terms: -8e + 8e = 0
5 + 8e + 3e2 = 0

Factor a trinomial.
(5 + 3e)(1 + e) = 0

Subproblem 1
Set the factor '(5 + 3e)' equal to zero and attempt to solve:

Simplifying
5 + 3e = 0

Solving
5 + 3e = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3e = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3e = 0 + -5
3e = 0 + -5

Combine like terms: 0 + -5 = -5
3e = -5

Divide each side by '3'.
e = -1.666666667

Simplifying
e = -1.666666667
Subproblem 2
Set the factor '(1 + e)' equal to zero and attempt to solve:

Simplifying
1 + e = 0

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

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

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

Simplifying
e = -1
Solution
e = {-1.666666667, -1}