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

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

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

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

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

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

Combine like terms: -2x + -1x = -3x
(2 + -3x + x2) = 6

Solving
2 + -3x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
2 + -6 + -3x + x2 = 6 + -6

Combine like terms: 2 + -6 = -4
-4 + -3x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-4 + -3x + x2 = 0

Factor a trinomial.
(-1 + -1x)(4 + -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 '(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 = {-1, 4}