x^2-4x+6=11

Solution for x^2-4x+6=11 equation:

Simplifying
x2 + -4x + 6 = 11

Reorder the terms:
6 + -4x + x2 = 11

Solving
6 + -4x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
6 + -11 + -4x + x2 = 11 + -11

Combine like terms: 6 + -11 = -5
-5 + -4x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-5 + -4x + x2 = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 5}