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

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


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

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

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

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

Combine like terms: -8w + 7w = -1w
3(56 + -1w + -1w2) = 0
(56 * 3 + -1w * 3 + -1w2 * 3) = 0
(168 + -3w + -3w2) = 0

Solving
168 + -3w + -3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(56 + -1w + -1w2) = 0

Factor a trinomial.
3((7 + -1w)(8 + w)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7

Subproblem 2
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
Solution
w = {7, -8}

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