(20w)+w(30+w)=5000

Solution for (20w)+w(30+w)=5000 equation:

Simplifying
(20w) + w(30 + w) = 5000
(20w) + (30 * w + w * w) = 5000
(20w) + (30w + w2) = 5000

Combine like terms: (20w) + 30w = 50w
50w + w2 = 5000

Solving
50w + w2 = 5000

Solving for variable 'w'.

Reorder the terms:
-5000 + 50w + w2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-5000 + 50w + w2 = 0

Factor a trinomial.
(-100 + -1w)(50 + -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 '(50 + -1w)' equal to zero and attempt to solve:

Simplifying
50 + -1w = 0

Solving
50 + -1w = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1w = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1w = 0 + -50
-1w = 0 + -50

Combine like terms: 0 + -50 = -50
-1w = -50

Divide each side by '-1'.
w = 50

Simplifying
w = 50
Solution
w = {-100, 50}