40=(w+3)w

Solution for 40=(w+3)w equation:

Simplifying
40 = (w + 3) * w

Reorder the terms:
40 = (3 + w) * w

Reorder the terms for easier multiplication:
40 = w(3 + w)
40 = (3 * w + w * w)
40 = (3w + w2)

Solving
40 = 3w + w2

Solving for variable 'w'.

Reorder the terms:
40 + -3w + -1w2 = 3w + -3w + w2 + -1w2

Combine like terms: 3w + -3w = 0
40 + -3w + -1w2 = 0 + w2 + -1w2
40 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
40 + -3w + -1w2 = 0

Factor a trinomial.
(5 + -1w)(8 + w) = 0

Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Subproblem 2
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8
Solution
w = {5, -8}