2w^2-5w+37=w^2+6w+9

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Solution for 2w^2-5w+37=w^2+6w+9 equation: 


Simplifying
2w2 + -5w + 37 = w2 + 6w + 9

Reorder the terms:
37 + -5w + 2w2 = w2 + 6w + 9

Reorder the terms:
37 + -5w + 2w2 = 9 + 6w + w2

Solving
37 + -5w + 2w2 = 9 + 6w + w2

Solving for variable 'w'.

Reorder the terms:
37 + -9 + -5w + -6w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 37 + -9 = 28
28 + -5w + -6w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: -5w + -6w = -11w
28 + -11w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
28 + -11w + 1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Reorder the terms:
28 + -11w + 1w2 = 9 + -9 + 6w + -6w + w2 + -1w2

Combine like terms: 9 + -9 = 0
28 + -11w + 1w2 = 0 + 6w + -6w + w2 + -1w2
28 + -11w + 1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
28 + -11w + 1w2 = 0 + w2 + -1w2
28 + -11w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
28 + -11w + 1w2 = 0

Factor a trinomial.
(4 + -1w)(7 + -1w) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {4, 7}

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