8-4w=169+26w+w^2

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Solution for 8-4w=169+26w+w^2 equation: 


Simplifying
8 + -4w = 169 + 26w + w2

Solving
8 + -4w = 169 + 26w + w2

Solving for variable 'w'.

Reorder the terms:
8 + -169 + -4w + -26w + -1w2 = 169 + 26w + w2 + -169 + -26w + -1w2

Combine like terms: 8 + -169 = -161
-161 + -4w + -26w + -1w2 = 169 + 26w + w2 + -169 + -26w + -1w2

Combine like terms: -4w + -26w = -30w
-161 + -30w + -1w2 = 169 + 26w + w2 + -169 + -26w + -1w2

Reorder the terms:
-161 + -30w + -1w2 = 169 + -169 + 26w + -26w + w2 + -1w2

Combine like terms: 169 + -169 = 0
-161 + -30w + -1w2 = 0 + 26w + -26w + w2 + -1w2
-161 + -30w + -1w2 = 26w + -26w + w2 + -1w2

Combine like terms: 26w + -26w = 0
-161 + -30w + -1w2 = 0 + w2 + -1w2
-161 + -30w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-161 + -30w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(161 + 30w + w2) = 0

Factor a trinomial.
-1((23 + w)(7 + w)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(23 + w)' equal to zero and attempt to solve:

Simplifying
23 + w = 0

Solving
23 + w = 0

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

Add '-23' to each side of the equation.
23 + -23 + w = 0 + -23

Combine like terms: 23 + -23 = 0
0 + w = 0 + -23
w = 0 + -23

Combine like terms: 0 + -23 = -23
w = -23

Simplifying
w = -23

Subproblem 2
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

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

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

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

Simplifying
w = -7
Solution
w = {-23, -7}

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