(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 = 9w
(-56 + 9w + 2w2) = 0

Solving
-56 + 9w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8 + -1w)(7 + -2w) = 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 '(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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