4e^2+5e(2e+9)=

Solution for 4e^2+5e(2e+9)= equation:

Simplifying
4e2 + 5e(2e + 9) = 0

Reorder the terms:
4e2 + 5e(9 + 2e) = 0
4e2 + (9 * 5e + 2e * 5e) = 0
4e2 + (45e + 10e2) = 0

Reorder the terms:
45e + 4e2 + 10e2 = 0

Combine like terms: 4e2 + 10e2 = 14e2
45e + 14e2 = 0

Solving
45e + 14e2 = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), 'e'.
e(45 + 14e) = 0

Subproblem 1
Set the factor 'e' equal to zero and attempt to solve:

Simplifying
e = 0

Solving
e = 0

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

Simplifying
e = 0
Subproblem 2
Set the factor '(45 + 14e)' equal to zero and attempt to solve:

Simplifying
45 + 14e = 0

Solving
45 + 14e = 0

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

Add '-45' to each side of the equation.
45 + -45 + 14e = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 14e = 0 + -45
14e = 0 + -45

Combine like terms: 0 + -45 = -45
14e = -45

Divide each side by '14'.
e = -3.214285714

Simplifying
e = -3.214285714
Solution
e = {0, -3.214285714}