(w-1)(w-2)=6

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

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

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

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

Multiply (-1 + w) * (-2 + w)
(-1(-2 + w) + w(-2 + w)) = 6
((-2 * -1 + w * -1) + w(-2 + w)) = 6
((2 + -1w) + w(-2 + w)) = 6
(2 + -1w + (-2 * w + w * w)) = 6
(2 + -1w + (-2w + w2)) = 6

Combine like terms: -1w + -2w = -3w
(2 + -3w + w2) = 6

Solving
2 + -3w + w2 = 6

Solving for variable 'w'.

Reorder the terms:
2 + -6 + -3w + w2 = 6 + -6

Combine like terms: 2 + -6 = -4
-4 + -3w + w2 = 6 + -6

Combine like terms: 6 + -6 = 0
-4 + -3w + w2 = 0

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

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

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

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

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

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

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

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

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

Simplifying
w = 4
Solution
w = {-1, 4}