(3w-7)(8-w)=0

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Solution for (3w-7)(8-w)=0 equation: 


Simplifying
(3w + -7)(8 + -1w) = 0

Reorder the terms:
(-7 + 3w)(8 + -1w) = 0

Multiply (-7 + 3w) * (8 + -1w)
(-7(8 + -1w) + 3w * (8 + -1w)) = 0
((8 * -7 + -1w * -7) + 3w * (8 + -1w)) = 0
((-56 + 7w) + 3w * (8 + -1w)) = 0
(-56 + 7w + (8 * 3w + -1w * 3w)) = 0
(-56 + 7w + (24w + -3w2)) = 0

Combine like terms: 7w + 24w = 31w
(-56 + 31w + -3w2) = 0

Solving
-56 + 31w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8 + w)(7 + -3w) = 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 + -3w)' equal to zero and attempt to solve:

Simplifying
7 + -3w = 0

Solving
7 + -3w = 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 + -3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3w = 0 + -7
-3w = 0 + -7

Combine like terms: 0 + -7 = -7
-3w = -7

Divide each side by '-3'.
w = 2.333333333

Simplifying
w = 2.333333333
Solution
w = {8, 2.333333333}

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