2w^2+13w+19=w^2+6w+9

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Solution for 2w^2+13w+19=w^2+6w+9 equation: 


Simplifying
2w2 + 13w + 19 = w2 + 6w + 9

Reorder the terms:
19 + 13w + 2w2 = w2 + 6w + 9

Reorder the terms:
19 + 13w + 2w2 = 9 + 6w + w2

Solving
19 + 13w + 2w2 = 9 + 6w + w2

Solving for variable 'w'.

Reorder the terms:
19 + -9 + 13w + -6w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 19 + -9 = 10
10 + 13w + -6w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 13w + -6w = 7w
10 + 7w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
10 + 7w + 1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Reorder the terms:
10 + 7w + 1w2 = 9 + -9 + 6w + -6w + w2 + -1w2

Combine like terms: 9 + -9 = 0
10 + 7w + 1w2 = 0 + 6w + -6w + w2 + -1w2
10 + 7w + 1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
10 + 7w + 1w2 = 0 + w2 + -1w2
10 + 7w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
10 + 7w + 1w2 = 0

Factor a trinomial.
(5 + w)(2 + w) = 0


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

Simplifying
5 + w = 0

Solving
5 + w = 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 + w = 0 + -5

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

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

Simplifying
w = -5

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

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

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

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

Simplifying
w = -2
Solution
w = {-5, -2}

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