e^2=16e-48

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

Simplifying
e2 = 16e + -48

Reorder the terms:
e2 = -48 + 16e

Solving
e2 = -48 + 16e

Solving for variable 'e'.

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

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

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

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

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

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

Simplifying
12 + -1e = 0

Solving
12 + -1e = 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 + -1e = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1e = 0 + -12
-1e = 0 + -12

Combine like terms: 0 + -12 = -12
-1e = -12

Divide each side by '-1'.
e = 12

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