6000=w(40+w)

Solution for 6000=w(40+w) equation:

Simplifying
6000 = w(40 + w)
6000 = (40 * w + w * w)
6000 = (40w + w2)

Solving
6000 = 40w + w2

Solving for variable 'w'.

Reorder the terms:
6000 + -40w + -1w2 = 40w + -40w + w2 + -1w2

Combine like terms: 40w + -40w = 0
6000 + -40w + -1w2 = 0 + w2 + -1w2
6000 + -40w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
6000 + -40w + -1w2 = 0

Factor a trinomial.
(60 + -1w)(100 + w) = 0

Subproblem 1
Set the factor '(60 + -1w)' equal to zero and attempt to solve:

Simplifying
60 + -1w = 0

Solving
60 + -1w = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1w = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1w = 0 + -60
-1w = 0 + -60

Combine like terms: 0 + -60 = -60
-1w = -60

Divide each side by '-1'.
w = 60

Simplifying
w = 60
Subproblem 2
Set the factor '(100 + w)' equal to zero and attempt to solve:

Simplifying
100 + w = 0

Solving
100 + w = 0

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

Add '-100' to each side of the equation.
100 + -100 + w = 0 + -100

Combine like terms: 100 + -100 = 0
0 + w = 0 + -100
w = 0 + -100

Combine like terms: 0 + -100 = -100
w = -100

Simplifying
w = -100
Solution
w = {60, -100}