(40+w)(w)=6000

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

Simplifying
(40 + w)(w) = 6000

Reorder the terms for easier multiplication:
w(40 + w) = 6000
(40 * w + w * w) = 6000
(40w + w2) = 6000

Solving
40w + w2 = 6000

Solving for variable 'w'.

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

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

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

Subproblem 1
Set the factor '(-100 + -1w)' equal to zero and attempt to solve:

Simplifying
-100 + -1w = 0

Solving
-100 + -1w = 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 + -1w = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1w = 0 + 100
-1w = 0 + 100

Combine like terms: 0 + 100 = 100
-1w = 100

Divide each side by '-1'.
w = -100

Simplifying
w = -100
Subproblem 2
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
Solution
w = {-100, 60}