4W+W^2=165

Solution for 4W+W^2=165 equation:

Simplifying
4W + W2 = 165

Solving
4W + W2 = 165

Solving for variable 'W'.

Reorder the terms:
-165 + 4W + W2 = 165 + -165

Combine like terms: 165 + -165 = 0
-165 + 4W + W2 = 0

Factor a trinomial.
(-15 + -1W)(11 + -1W) = 0

Subproblem 1
Set the factor '(-15 + -1W)' equal to zero and attempt to solve:

Simplifying
-15 + -1W = 0

Solving
-15 + -1W = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1W = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1W = 0 + 15
-1W = 0 + 15

Combine like terms: 0 + 15 = 15
-1W = 15

Divide each side by '-1'.
W = -15

Simplifying
W = -15
Subproblem 2
Set the factor '(11 + -1W)' equal to zero and attempt to solve:

Simplifying
11 + -1W = 0

Solving
11 + -1W = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1W = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1W = 0 + -11
-1W = 0 + -11

Combine like terms: 0 + -11 = -11
-1W = -11

Divide each side by '-1'.
W = 11

Simplifying
W = 11
Solution
W = {-15, 11}