(2+w)(5w+8)=0

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Solution for (2+w)(5w+8)=0 equation: 


Simplifying
(2 + w)(5w + 8) = 0

Reorder the terms:
(2 + w)(8 + 5w) = 0

Multiply (2 + w) * (8 + 5w)
(2(8 + 5w) + w(8 + 5w)) = 0
((8 * 2 + 5w * 2) + w(8 + 5w)) = 0
((16 + 10w) + w(8 + 5w)) = 0
(16 + 10w + (8 * w + 5w * w)) = 0
(16 + 10w + (8w + 5w2)) = 0

Combine like terms: 10w + 8w = 18w
(16 + 18w + 5w2) = 0

Solving
16 + 18w + 5w2 = 0

Solving for variable 'w'.

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


Subproblem 1
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2

Subproblem 2
Set the factor '(8 + 5w)' equal to zero and attempt to solve:

Simplifying
8 + 5w = 0

Solving
8 + 5w = 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 + 5w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5w = 0 + -8
5w = 0 + -8

Combine like terms: 0 + -8 = -8
5w = -8

Divide each side by '5'.
w = -1.6

Simplifying
w = -1.6
Solution
w = {-2, -1.6}

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