3w-w^2=2

Solution for 3w-w^2=2 equation:

Simplifying
3w + -1w2 = 2

Solving
3w + -1w2 = 2

Solving for variable 'w'.

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

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

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

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

Simplifying
-2 + w = 0

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

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

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

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