2w^2-18w+37=w^2-10w+25

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Solution for 2w^2-18w+37=w^2-10w+25 equation: 


Simplifying
2w2 + -18w + 37 = w2 + -10w + 25

Reorder the terms:
37 + -18w + 2w2 = w2 + -10w + 25

Reorder the terms:
37 + -18w + 2w2 = 25 + -10w + w2

Solving
37 + -18w + 2w2 = 25 + -10w + w2

Solving for variable 'w'.

Reorder the terms:
37 + -25 + -18w + 10w + 2w2 + -1w2 = 25 + -10w + w2 + -25 + 10w + -1w2

Combine like terms: 37 + -25 = 12
12 + -18w + 10w + 2w2 + -1w2 = 25 + -10w + w2 + -25 + 10w + -1w2

Combine like terms: -18w + 10w = -8w
12 + -8w + 2w2 + -1w2 = 25 + -10w + w2 + -25 + 10w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
12 + -8w + 1w2 = 25 + -10w + w2 + -25 + 10w + -1w2

Reorder the terms:
12 + -8w + 1w2 = 25 + -25 + -10w + 10w + w2 + -1w2

Combine like terms: 25 + -25 = 0
12 + -8w + 1w2 = 0 + -10w + 10w + w2 + -1w2
12 + -8w + 1w2 = -10w + 10w + w2 + -1w2

Combine like terms: -10w + 10w = 0
12 + -8w + 1w2 = 0 + w2 + -1w2
12 + -8w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
12 + -8w + 1w2 = 0

Factor a trinomial.
(2 + -1w)(6 + -1w) = 0


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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2

Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {2, 6}

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