5e^2(-3e^2-2e-3)=

Solution for 5e^2(-3e^2-2e-3)= equation:

Simplifying
5e2(-3e2 + -2e + -3) = 0

Reorder the terms:
5e2(-3 + -2e + -3e2) = 0
(-3 * 5e2 + -2e * 5e2 + -3e2 * 5e2) = 0
(-15e2 + -10e3 + -15e4) = 0

Solving
-15e2 + -10e3 + -15e4 = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), '-5e2'.
-5e2(3 + 2e + 3e2) = 0

Ignore the factor -5.
Subproblem 1
Set the factor 'e2' equal to zero and attempt to solve:

Simplifying
e2 = 0

Solving
e2 = 0

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

Simplifying
e2 = 0

Take the square root of each side:
e = {0}
Subproblem 2
Set the factor '(3 + 2e + 3e2)' equal to zero and attempt to solve:

Simplifying
3 + 2e + 3e2 = 0

Solving
3 + 2e + 3e2 = 0

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

Divide each side by '3'.
1 + 0.6666666667e + e2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.6666666667e + -1 + e2 = 0 + -1

Reorder the terms:
1 + -1 + 0.6666666667e + e2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.6666666667e + e2 = 0 + -1
0.6666666667e + e2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.6666666667e + e2 = -1

The e term is 0.6666666667e.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667e + 0.1111111112 + e2 = -1 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667e + e2 = -1 + 0.1111111112

Combine like terms: -1 + 0.1111111112 = -0.8888888888
0.1111111112 + 0.6666666667e + e2 = -0.8888888888

Factor a perfect square on the left side:
(e + 0.3333333334)(e + 0.3333333334) = -0.8888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
e = {0}