x(x-6)+1=x-11

Solution for x(x-6)+1=x-11 equation:

Simplifying
x(x + -6) + 1 = x + -11

Reorder the terms:
x(-6 + x) + 1 = x + -11
(-6 * x + x * x) + 1 = x + -11
(-6x + x2) + 1 = x + -11

Reorder the terms:
1 + -6x + x2 = x + -11

Reorder the terms:
1 + -6x + x2 = -11 + x

Solving
1 + -6x + x2 = -11 + x

Solving for variable 'x'.

Reorder the terms:
1 + 11 + -6x + -1x + x2 = -11 + x + 11 + -1x

Combine like terms: 1 + 11 = 12
12 + -6x + -1x + x2 = -11 + x + 11 + -1x

Combine like terms: -6x + -1x = -7x
12 + -7x + x2 = -11 + x + 11 + -1x

Reorder the terms:
12 + -7x + x2 = -11 + 11 + x + -1x

Combine like terms: -11 + 11 = 0
12 + -7x + x2 = 0 + x + -1x
12 + -7x + x2 = x + -1x

Combine like terms: x + -1x = 0
12 + -7x + x2 = 0

Factor a trinomial.
(3 + -1x)(4 + -1x) = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

Simplifying
x = 3
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3, 4}