w(3+w)=40

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


Simplifying
w(3 + w) = 40
(3 * w + w * w) = 40
(3w + w2) = 40

Solving
3w + w2 = 40

Solving for variable 'w'.

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

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

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


Subproblem 1
Set the factor '(-8 + -1w)' equal to zero and attempt to solve:

Simplifying
-8 + -1w = 0

Solving
-8 + -1w = 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 + -1w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1w = 0 + 8
-1w = 0 + 8

Combine like terms: 0 + 8 = 8
-1w = 8

Divide each side by '-1'.
w = -8

Simplifying
w = -8

Subproblem 2
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
Solution
w = {-8, 5}

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