(w-13)(w-13)=16

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Solution for (w-13)(w-13)=16 equation: 


Simplifying
(w + -13)(w + -13) = 16

Reorder the terms:
(-13 + w)(w + -13) = 16

Reorder the terms:
(-13 + w)(-13 + w) = 16

Multiply (-13 + w) * (-13 + w)
(-13(-13 + w) + w(-13 + w)) = 16
((-13 * -13 + w * -13) + w(-13 + w)) = 16
((169 + -13w) + w(-13 + w)) = 16
(169 + -13w + (-13 * w + w * w)) = 16
(169 + -13w + (-13w + w2)) = 16

Combine like terms: -13w + -13w = -26w
(169 + -26w + w2) = 16

Solving
169 + -26w + w2 = 16

Solving for variable 'w'.

Reorder the terms:
169 + -16 + -26w + w2 = 16 + -16

Combine like terms: 169 + -16 = 153
153 + -26w + w2 = 16 + -16

Combine like terms: 16 + -16 = 0
153 + -26w + w2 = 0

Factor a trinomial.
(9 + -1w)(17 + -1w) = 0


Subproblem 1
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9

Subproblem 2
Set the factor '(17 + -1w)' equal to zero and attempt to solve:

Simplifying
17 + -1w = 0

Solving
17 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-17' to each side of the equation.
17 + -17 + -1w = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1w = 0 + -17
-1w = 0 + -17

Combine like terms: 0 + -17 = -17
-1w = -17

Divide each side by '-1'.
w = 17

Simplifying
w = 17
Solution
w = {9, 17}

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