(2w+1)(8-w)=0

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Solution for (2w+1)(8-w)=0 equation: 


Simplifying
(2w + 1)(8 + -1w) = 0

Reorder the terms:
(1 + 2w)(8 + -1w) = 0

Multiply (1 + 2w) * (8 + -1w)
(1(8 + -1w) + 2w * (8 + -1w)) = 0
((8 * 1 + -1w * 1) + 2w * (8 + -1w)) = 0
((8 + -1w) + 2w * (8 + -1w)) = 0
(8 + -1w + (8 * 2w + -1w * 2w)) = 0
(8 + -1w + (16w + -2w2)) = 0

Combine like terms: -1w + 16w = 15w
(8 + 15w + -2w2) = 0

Solving
8 + 15w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + -1w)(1 + 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 '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {8, -0.5}

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