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

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


Simplifying
(5 + -1w)(5w + 8) = 0

Reorder the terms:
(5 + -1w)(8 + 5w) = 0

Multiply (5 + -1w) * (8 + 5w)
(5(8 + 5w) + -1w * (8 + 5w)) = 0
((8 * 5 + 5w * 5) + -1w * (8 + 5w)) = 0
((40 + 25w) + -1w * (8 + 5w)) = 0
(40 + 25w + (8 * -1w + 5w * -1w)) = 0
(40 + 25w + (-8w + -5w2)) = 0

Combine like terms: 25w + -8w = 17w
(40 + 17w + -5w2) = 0

Solving
40 + 17w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + -1w)(8 + 5w) = 0


Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 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 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5

Subproblem 2
Set the factor '(8 + 5w)' equal to zero and attempt to solve:

Simplifying
8 + 5w = 0

Solving
8 + 5w = 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 + 5w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5w = 0 + -8
5w = 0 + -8

Combine like terms: 0 + -8 = -8
5w = -8

Divide each side by '5'.
w = -1.6

Simplifying
w = -1.6
Solution
w = {5, -1.6}

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