e^2-10e+21=0

Solution for e^2-10e+21=0 equation:

Simplifying
e2 + -10e + 21 = 0

Reorder the terms:
21 + -10e + e2 = 0

Solving
21 + -10e + e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(3 + -1e)(7 + -1e) = 0

Subproblem 1
Set the factor '(3 + -1e)' equal to zero and attempt to solve:

Simplifying
3 + -1e = 0

Solving
3 + -1e = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1e = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1e = 0 + -3
-1e = 0 + -3

Combine like terms: 0 + -3 = -3
-1e = -3

Divide each side by '-1'.
e = 3

Simplifying
e = 3
Subproblem 2
Set the factor '(7 + -1e)' equal to zero and attempt to solve:

Simplifying
7 + -1e = 0

Solving
7 + -1e = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1e = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1e = 0 + -7
-1e = 0 + -7

Combine like terms: 0 + -7 = -7
-1e = -7

Divide each side by '-1'.
e = 7

Simplifying
e = 7
Solution
e = {3, 7}