=48-16e+e^2

Solution for =48-16e+e^2 equation:

Simplifying
0 = 48 + -16e + e2

Solving
0 = 48 + -16e + e2

Solving for variable 'e'.

Combine like terms: 0 + -48 = -48
-48 + 16e + -1e2 = 48 + -16e + e2 + -48 + 16e + -1e2

Reorder the terms:
-48 + 16e + -1e2 = 48 + -48 + -16e + 16e + e2 + -1e2

Combine like terms: 48 + -48 = 0
-48 + 16e + -1e2 = 0 + -16e + 16e + e2 + -1e2
-48 + 16e + -1e2 = -16e + 16e + e2 + -1e2

Combine like terms: -16e + 16e = 0
-48 + 16e + -1e2 = 0 + e2 + -1e2
-48 + 16e + -1e2 = e2 + -1e2

Combine like terms: e2 + -1e2 = 0
-48 + 16e + -1e2 = 0

Factor a trinomial.
(-12 + e)(4 + -1e) = 0

Subproblem 1
Set the factor '(-12 + e)' equal to zero and attempt to solve:

Simplifying
-12 + e = 0

Solving
-12 + e = 0

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

Add '12' to each side of the equation.
-12 + 12 + e = 0 + 12

Combine like terms: -12 + 12 = 0
0 + e = 0 + 12
e = 0 + 12

Combine like terms: 0 + 12 = 12
e = 12

Simplifying
e = 12
Subproblem 2
Set the factor '(4 + -1e)' equal to zero and attempt to solve:

Simplifying
4 + -1e = 0

Solving
4 + -1e = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1e = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1e = 0 + -4
-1e = 0 + -4

Combine like terms: 0 + -4 = -4
-1e = -4

Divide each side by '-1'.
e = 4

Simplifying
e = 4
Solution
e = {12, 4}