(2w+3)(8-w)=0

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Solution for (2w+3)(8-w)=0 equation: 


Simplifying
(2w + 3)(8 + -1w) = 0

Reorder the terms:
(3 + 2w)(8 + -1w) = 0

Multiply (3 + 2w) * (8 + -1w)
(3(8 + -1w) + 2w * (8 + -1w)) = 0
((8 * 3 + -1w * 3) + 2w * (8 + -1w)) = 0
((24 + -3w) + 2w * (8 + -1w)) = 0
(24 + -3w + (8 * 2w + -1w * 2w)) = 0
(24 + -3w + (16w + -2w2)) = 0

Combine like terms: -3w + 16w = 13w
(24 + 13w + -2w2) = 0

Solving
24 + 13w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + -1w)(3 + 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 '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {8, -1.5}

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