4w+1-w^2+2w-1=0

Solution for 4w+1-w^2+2w-1=0 equation:

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

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

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

Combine like terms: 4w + 2w = 6w
6w + -1w2 = 0

Solving
6w + -1w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w'.
w(6 + -1w) = 0

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {0, 6}