2w^2-3w-1-w^2+2w-1=0

Solution for 2w^2-3w-1-w^2+2w-1=0 equation:

Simplifying
2w2 + -3w + -1 + -1w2 + 2w + -1 = 0

Reorder the terms:
-1 + -1 + -3w + 2w + 2w2 + -1w2 = 0

Combine like terms: -1 + -1 = -2
-2 + -3w + 2w + 2w2 + -1w2 = 0

Combine like terms: -3w + 2w = -1w
-2 + -1w + 2w2 + -1w2 = 0

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

Solving
-2 + -1w + 1w2 = 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}