4e-3(2e-2)=3(e+8)e

Solution for 4e-3(2e-2)=3(e+8)e equation:

Simplifying
4e + -3(2e + -2) = 3(e + 8) * e

Reorder the terms:
4e + -3(-2 + 2e) = 3(e + 8) * e
4e + (-2 * -3 + 2e * -3) = 3(e + 8) * e
4e + (6 + -6e) = 3(e + 8) * e

Reorder the terms:
6 + 4e + -6e = 3(e + 8) * e

Combine like terms: 4e + -6e = -2e
6 + -2e = 3(e + 8) * e

Reorder the terms:
6 + -2e = 3(8 + e) * e

Reorder the terms for easier multiplication:
6 + -2e = 3e(8 + e)
6 + -2e = (8 * 3e + e * 3e)
6 + -2e = (24e + 3e2)

Solving
6 + -2e = 24e + 3e2

Solving for variable 'e'.

Combine like terms: -2e + -24e = -26e
6 + -26e + -3e2 = 24e + 3e2 + -24e + -3e2

Reorder the terms:
6 + -26e + -3e2 = 24e + -24e + 3e2 + -3e2

Combine like terms: 24e + -24e = 0
6 + -26e + -3e2 = 0 + 3e2 + -3e2
6 + -26e + -3e2 = 3e2 + -3e2

Combine like terms: 3e2 + -3e2 = 0
6 + -26e + -3e2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2 + 8.666666667e + e2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8.666666667e + 2 + e2 = 0 + 2

Reorder the terms:
-2 + 2 + 8.666666667e + e2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8.666666667e + e2 = 0 + 2
8.666666667e + e2 = 0 + 2

Combine like terms: 0 + 2 = 2
8.666666667e + e2 = 2

The e term is 8.666666667e.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667e + 18.77777778 + e2 = 2 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667e + e2 = 2 + 18.77777778

Combine like terms: 2 + 18.77777778 = 20.77777778
18.77777778 + 8.666666667e + e2 = 20.77777778

Factor a perfect square on the left side:
(e + 4.333333334)(e + 4.333333334) = 20.77777778

Calculate the square root of the right side: 4.558264777

Break this problem into two subproblems by setting 
(e + 4.333333334) equal to 4.558264777 and -4.558264777.

Subproblem 1
e + 4.333333334 = 4.558264777

Simplifying
e + 4.333333334 = 4.558264777

Reorder the terms:
4.333333334 + e = 4.558264777

Solving
4.333333334 + e = 4.558264777

Solving for variable 'e'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + e = 4.558264777 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + e = 4.558264777 + -4.333333334
e = 4.558264777 + -4.333333334

Combine like terms: 4.558264777 + -4.333333334 = 0.224931443
e = 0.224931443

Simplifying
e = 0.224931443

Subproblem 2
e + 4.333333334 = -4.558264777

Simplifying
e + 4.333333334 = -4.558264777

Reorder the terms:
4.333333334 + e = -4.558264777

Solving
4.333333334 + e = -4.558264777

Solving for variable 'e'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + e = -4.558264777 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + e = -4.558264777 + -4.333333334
e = -4.558264777 + -4.333333334

Combine like terms: -4.558264777 + -4.333333334 = -8.891598111
e = -8.891598111

Simplifying
e = -8.891598111

Solution
The solution to the problem is based on the solutions
from the subproblems.
e = {0.224931443, -8.891598111}