6000=(40+w)w

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


Simplifying
6000 = (40 + w) * w

Reorder the terms for easier multiplication:
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}

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