0=-w^2+4w-3

Solution for 0=-w^2+4w-3 equation:

Simplifying
0 = -1w2 + 4w + -3

Reorder the terms:
0 = -3 + 4w + -1w2

Solving
0 = -3 + 4w + -1w2

Solving for variable 'w'.

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

Reorder the terms:
3 + -4w + w2 = -3 + 3 + 4w + -4w + -1w2 + w2

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

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

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

Factor a trinomial.
(1 + -1w)(3 + -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 '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

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

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

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {1, 3}