a^2-20a+41=5

Solution for a^2-20a+41=5 equation:

Simplifying
a2 + -20a + 41 = 5

Reorder the terms:
41 + -20a + a2 = 5

Solving
41 + -20a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
41 + -5 + -20a + a2 = 5 + -5

Combine like terms: 41 + -5 = 36
36 + -20a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
36 + -20a + a2 = 0

Factor a trinomial.
(2 + -1a)(18 + -1a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Subproblem 2
Set the factor '(18 + -1a)' equal to zero and attempt to solve:

Simplifying
18 + -1a = 0

Solving
18 + -1a = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1a = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1a = 0 + -18
-1a = 0 + -18

Combine like terms: 0 + -18 = -18
-1a = -18

Divide each side by '-1'.
a = 18

Simplifying
a = 18
Solution
a = {2, 18}