(4w+7)(8-w)=0

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Solution for (4w+7)(8-w)=0 equation: 


Simplifying
(4w + 7)(8 + -1w) = 0

Reorder the terms:
(7 + 4w)(8 + -1w) = 0

Multiply (7 + 4w) * (8 + -1w)
(7(8 + -1w) + 4w * (8 + -1w)) = 0
((8 * 7 + -1w * 7) + 4w * (8 + -1w)) = 0
((56 + -7w) + 4w * (8 + -1w)) = 0
(56 + -7w + (8 * 4w + -1w * 4w)) = 0
(56 + -7w + (32w + -4w2)) = 0

Combine like terms: -7w + 32w = 25w
(56 + 25w + -4w2) = 0

Solving
56 + 25w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + -1w)(7 + 4w) = 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 '(7 + 4w)' equal to zero and attempt to solve:

Simplifying
7 + 4w = 0

Solving
7 + 4w = 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 + 4w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4w = 0 + -7
4w = 0 + -7

Combine like terms: 0 + -7 = -7
4w = -7

Divide each side by '4'.
w = -1.75

Simplifying
w = -1.75
Solution
w = {8, -1.75}

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