(4e+2)(2e+9)=

Solution for (4e+2)(2e+9)= equation:

Simplifying
(4e + 2)(2e + 9) = 0

Reorder the terms:
(2 + 4e)(2e + 9) = 0

Reorder the terms:
(2 + 4e)(9 + 2e) = 0

Multiply (2 + 4e) * (9 + 2e)
(2(9 + 2e) + 4e * (9 + 2e)) = 0
((9 * 2 + 2e * 2) + 4e * (9 + 2e)) = 0
((18 + 4e) + 4e * (9 + 2e)) = 0
(18 + 4e + (9 * 4e + 2e * 4e)) = 0
(18 + 4e + (36e + 8e2)) = 0

Combine like terms: 4e + 36e = 40e
(18 + 40e + 8e2) = 0

Solving
18 + 40e + 8e2 = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 20e + 4e2) = 0

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

Ignore the factor 2.
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 '(1 + 2e)' equal to zero and attempt to solve:

Simplifying
1 + 2e = 0

Solving
1 + 2e = 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 + 2e = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2e = 0 + -1
2e = 0 + -1

Combine like terms: 0 + -1 = -1
2e = -1

Divide each side by '2'.
e = -0.5

Simplifying
e = -0.5
Solution
e = {-4.5, -0.5}