(w-2)(w+1)=0

Solution for (w-2)(w+1)=0 equation:

Simplifying
(w + -2)(w + 1) = 0

Reorder the terms:
(-2 + w)(w + 1) = 0

Reorder the terms:
(-2 + w)(1 + w) = 0

Multiply (-2 + w) * (1 + w)
(-2(1 + w) + w(1 + w)) = 0
((1 * -2 + w * -2) + w(1 + w)) = 0
((-2 + -2w) + w(1 + w)) = 0
(-2 + -2w + (1 * w + w * w)) = 0
(-2 + -2w + (1w + w2)) = 0

Combine like terms: -2w + 1w = -1w
(-2 + -1w + w2) = 0

Solving
-2 + -1w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(2 + -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 '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

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

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

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

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

Simplifying
w = 2
Solution
w = {-1, 2}