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

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


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

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

Multiply (5 + 2w) * (8 + w)
(5(8 + w) + 2w * (8 + w)) = 0
((8 * 5 + w * 5) + 2w * (8 + w)) = 0
((40 + 5w) + 2w * (8 + w)) = 0
(40 + 5w + (8 * 2w + w * 2w)) = 0
(40 + 5w + (16w + 2w2)) = 0

Combine like terms: 5w + 16w = 21w
(40 + 21w + 2w2) = 0

Solving
40 + 21w + 2w2 = 0

Solving for variable 'w'.

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


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

Simplifying
8 + w = 0

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

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

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

Simplifying
w = -8

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

Simplifying
5 + 2w = 0

Solving
5 + 2w = 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 + 2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2w = 0 + -5
2w = 0 + -5

Combine like terms: 0 + -5 = -5
2w = -5

Divide each side by '2'.
w = -2.5

Simplifying
w = -2.5
Solution
w = {-8, -2.5}

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