(3e+2)(4e+1)=

Solution for (3e+2)(4e+1)= equation:

Simplifying
(3e + 2)(4e + 1) = 0

Reorder the terms:
(2 + 3e)(4e + 1) = 0

Reorder the terms:
(2 + 3e)(1 + 4e) = 0

Multiply (2 + 3e) * (1 + 4e)
(2(1 + 4e) + 3e * (1 + 4e)) = 0
((1 * 2 + 4e * 2) + 3e * (1 + 4e)) = 0
((2 + 8e) + 3e * (1 + 4e)) = 0
(2 + 8e + (1 * 3e + 4e * 3e)) = 0
(2 + 8e + (3e + 12e2)) = 0

Combine like terms: 8e + 3e = 11e
(2 + 11e + 12e2) = 0

Solving
2 + 11e + 12e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(2 + 3e)(1 + 4e) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 4e)' equal to zero and attempt to solve:

Simplifying
1 + 4e = 0

Solving
1 + 4e = 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 + 4e = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4e = 0 + -1
4e = 0 + -1

Combine like terms: 0 + -1 = -1
4e = -1

Divide each side by '4'.
e = -0.25

Simplifying
e = -0.25
Solution
e = {-0.6666666667, -0.25}