(x-6)(x-1)=-x-2

Solution for (x-6)(x-1)=-x-2 equation:

Simplifying
(x + -6)(x + -1) = -1x + -2

Reorder the terms:
(-6 + x)(x + -1) = -1x + -2

Reorder the terms:
(-6 + x)(-1 + x) = -1x + -2

Multiply (-6 + x) * (-1 + x)
(-6(-1 + x) + x(-1 + x)) = -1x + -2
((-1 * -6 + x * -6) + x(-1 + x)) = -1x + -2
((6 + -6x) + x(-1 + x)) = -1x + -2
(6 + -6x + (-1 * x + x * x)) = -1x + -2
(6 + -6x + (-1x + x2)) = -1x + -2

Combine like terms: -6x + -1x = -7x
(6 + -7x + x2) = -1x + -2

Reorder the terms:
6 + -7x + x2 = -2 + -1x

Solving
6 + -7x + x2 = -2 + -1x

Solving for variable 'x'.

Reorder the terms:
6 + 2 + -7x + x + x2 = -2 + -1x + 2 + x

Combine like terms: 6 + 2 = 8
8 + -7x + x + x2 = -2 + -1x + 2 + x

Combine like terms: -7x + x = -6x
8 + -6x + x2 = -2 + -1x + 2 + x

Reorder the terms:
8 + -6x + x2 = -2 + 2 + -1x + x

Combine like terms: -2 + 2 = 0
8 + -6x + x2 = 0 + -1x + x
8 + -6x + x2 = -1x + x

Combine like terms: -1x + x = 0
8 + -6x + x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

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

Simplifying
x = 2
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 = {2, 4}