x^2-16x+41=-x-9

Solution for x^2-16x+41=-x-9 equation:

Simplifying
x2 + -16x + 41 = -1x + -9

Reorder the terms:
41 + -16x + x2 = -1x + -9

Reorder the terms:
41 + -16x + x2 = -9 + -1x

Solving
41 + -16x + x2 = -9 + -1x

Solving for variable 'x'.

Reorder the terms:
41 + 9 + -16x + x + x2 = -9 + -1x + 9 + x

Combine like terms: 41 + 9 = 50
50 + -16x + x + x2 = -9 + -1x + 9 + x

Combine like terms: -16x + x = -15x
50 + -15x + x2 = -9 + -1x + 9 + x

Reorder the terms:
50 + -15x + x2 = -9 + 9 + -1x + x

Combine like terms: -9 + 9 = 0
50 + -15x + x2 = 0 + -1x + x
50 + -15x + x2 = -1x + x

Combine like terms: -1x + x = 0
50 + -15x + x2 = 0

Factor a trinomial.
(5 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {5, 10}