(3+W)W=460

Solution for (3+W)W=460 equation:

Simplifying
(3 + W) * W = 460

Reorder the terms for easier multiplication:
W(3 + W) = 460
(3 * W + W * W) = 460
(3W + W2) = 460

Solving
3W + W2 = 460

Solving for variable 'W'.

Reorder the terms:
-460 + 3W + W2 = 460 + -460

Combine like terms: 460 + -460 = 0
-460 + 3W + W2 = 0

Factor a trinomial.
(-23 + -1W)(20 + -1W) = 0

Subproblem 1
Set the factor '(-23 + -1W)' equal to zero and attempt to solve:

Simplifying
-23 + -1W = 0

Solving
-23 + -1W = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1W = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1W = 0 + 23
-1W = 0 + 23

Combine like terms: 0 + 23 = 23
-1W = 23

Divide each side by '-1'.
W = -23

Simplifying
W = -23
Subproblem 2
Set the factor '(20 + -1W)' equal to zero and attempt to solve:

Simplifying
20 + -1W = 0

Solving
20 + -1W = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1W = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1W = 0 + -20
-1W = 0 + -20

Combine like terms: 0 + -20 = -20
-1W = -20

Divide each side by '-1'.
W = 20

Simplifying
W = 20
Solution
W = {-23, 20}