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

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


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

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

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

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

Combine like terms: -7w + -8w = -15w
(56 + -15w + w2) = 0

Solving
56 + -15w + w2 = 0

Solving for variable 'w'.

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


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 + -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
Solution
w = {7, 8}

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