10e^3-5e^2=0

Solution for 10e^3-5e^2=0 equation:

Simplifying
10e3 + -5e2 = 0

Reorder the terms:
-5e2 + 10e3 = 0

Solving
-5e2 + 10e3 = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), '5e2'.
5e2(-1 + 2e) = 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 '(-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 = {0, 0.5}