2w^2-w+4w-2=0

Solution for 2w^2-w+4w-2=0 equation:

Simplifying
2w2 + -1w + 4w + -2 = 0

Reorder the terms:
-2 + -1w + 4w + 2w2 = 0

Combine like terms: -1w + 4w = 3w
-2 + 3w + 2w2 = 0

Solving
-2 + 3w + 2w2 = 0

Solving for variable 'w'.

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

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

Simplifying
1 + -2w = 0

Solving
1 + -2w = 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 + -2w = 0 + -1

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

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

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Solution
w = {-2, 0.5}