75=4e-5e(3+2e)

Solution for 75=4e-5e(3+2e) equation:

Simplifying
75 = 4e + -5e(3 + 2e)
75 = 4e + (3 * -5e + 2e * -5e)
75 = 4e + (-15e + -10e2)

Combine like terms: 4e + -15e = -11e
75 = -11e + -10e2

Solving
75 = -11e + -10e2

Solving for variable 'e'.

Reorder the terms:
75 + 11e + 10e2 = -11e + 11e + -10e2 + 10e2

Combine like terms: -11e + 11e = 0
75 + 11e + 10e2 = 0 + -10e2 + 10e2
75 + 11e + 10e2 = -10e2 + 10e2

Combine like terms: -10e2 + 10e2 = 0
75 + 11e + 10e2 = 0

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

Divide each side by '10'.
7.5 + 1.1e + e2 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + 1.1e + -7.5 + e2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + 1.1e + e2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + 1.1e + e2 = 0 + -7.5
1.1e + e2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
1.1e + e2 = -7.5

The e term is 1.1e.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1e + 0.3025 + e2 = -7.5 + 0.3025

Reorder the terms:
0.3025 + 1.1e + e2 = -7.5 + 0.3025

Combine like terms: -7.5 + 0.3025 = -7.1975
0.3025 + 1.1e + e2 = -7.1975

Factor a perfect square on the left side:
(e + 0.55)(e + 0.55) = -7.1975

Can't calculate square root of the right side.

The solution to this equation could not be determined.