2w^2-10w+1=w^2-8w+16

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Solution for 2w^2-10w+1=w^2-8w+16 equation: 


Simplifying
2w2 + -10w + 1 = w2 + -8w + 16

Reorder the terms:
1 + -10w + 2w2 = w2 + -8w + 16

Reorder the terms:
1 + -10w + 2w2 = 16 + -8w + w2

Solving
1 + -10w + 2w2 = 16 + -8w + w2

Solving for variable 'w'.

Reorder the terms:
1 + -16 + -10w + 8w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: 1 + -16 = -15
-15 + -10w + 8w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: -10w + 8w = -2w
-15 + -2w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-15 + -2w + 1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Reorder the terms:
-15 + -2w + 1w2 = 16 + -16 + -8w + 8w + w2 + -1w2

Combine like terms: 16 + -16 = 0
-15 + -2w + 1w2 = 0 + -8w + 8w + w2 + -1w2
-15 + -2w + 1w2 = -8w + 8w + w2 + -1w2

Combine like terms: -8w + 8w = 0
-15 + -2w + 1w2 = 0 + w2 + -1w2
-15 + -2w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-15 + -2w + 1w2 = 0

Factor a trinomial.
(-3 + -1w)(5 + -1w) = 0


Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3

Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-3, 5}

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