(2w+7)(8+w)=0

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Solution for (2w+7)(8+w)=0 equation: 


Simplifying
(2w + 7)(8 + w) = 0

Reorder the terms:
(7 + 2w)(8 + w) = 0

Multiply (7 + 2w) * (8 + w)
(7(8 + w) + 2w * (8 + w)) = 0
((8 * 7 + w * 7) + 2w * (8 + w)) = 0
((56 + 7w) + 2w * (8 + w)) = 0
(56 + 7w + (8 * 2w + w * 2w)) = 0
(56 + 7w + (16w + 2w2)) = 0

Combine like terms: 7w + 16w = 23w
(56 + 23w + 2w2) = 0

Solving
56 + 23w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + w)(7 + 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 '(7 + 2w)' equal to zero and attempt to solve:

Simplifying
7 + 2w = 0

Solving
7 + 2w = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2w = 0 + -7
2w = 0 + -7

Combine like terms: 0 + -7 = -7
2w = -7

Divide each side by '2'.
w = -3.5

Simplifying
w = -3.5
Solution
w = {-8, -3.5}

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