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

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


Simplifying
(8 + -1w)(2w + -7) = 0

Reorder the terms:
(8 + -1w)(-7 + 2w) = 0

Multiply (8 + -1w) * (-7 + 2w)
(8(-7 + 2w) + -1w * (-7 + 2w)) = 0
((-7 * 8 + 2w * 8) + -1w * (-7 + 2w)) = 0
((-56 + 16w) + -1w * (-7 + 2w)) = 0
(-56 + 16w + (-7 * -1w + 2w * -1w)) = 0
(-56 + 16w + (7w + -2w2)) = 0

Combine like terms: 16w + 7w = 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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