w^2-16=2w^2-17w+36

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Solution for w^2-16=2w^2-17w+36 equation: 


Simplifying
w2 + -16 = 2w2 + -17w + 36

Reorder the terms:
-16 + w2 = 2w2 + -17w + 36

Reorder the terms:
-16 + w2 = 36 + -17w + 2w2

Solving
-16 + w2 = 36 + -17w + 2w2

Solving for variable 'w'.

Reorder the terms:
-16 + -36 + 17w + w2 + -2w2 = 36 + -17w + 2w2 + -36 + 17w + -2w2

Combine like terms: -16 + -36 = -52
-52 + 17w + w2 + -2w2 = 36 + -17w + 2w2 + -36 + 17w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-52 + 17w + -1w2 = 36 + -17w + 2w2 + -36 + 17w + -2w2

Reorder the terms:
-52 + 17w + -1w2 = 36 + -36 + -17w + 17w + 2w2 + -2w2

Combine like terms: 36 + -36 = 0
-52 + 17w + -1w2 = 0 + -17w + 17w + 2w2 + -2w2
-52 + 17w + -1w2 = -17w + 17w + 2w2 + -2w2

Combine like terms: -17w + 17w = 0
-52 + 17w + -1w2 = 0 + 2w2 + -2w2
-52 + 17w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-52 + 17w + -1w2 = 0

Factor a trinomial.
(-13 + w)(4 + -1w) = 0


Subproblem 1
Set the factor '(-13 + w)' equal to zero and attempt to solve:

Simplifying
-13 + w = 0

Solving
-13 + w = 0

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

Add '13' to each side of the equation.
-13 + 13 + w = 0 + 13

Combine like terms: -13 + 13 = 0
0 + w = 0 + 13
w = 0 + 13

Combine like terms: 0 + 13 = 13
w = 13

Simplifying
w = 13

Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {13, 4}

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