w^2+10w+25=2w^2+19w+39

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Solution for w^2+10w+25=2w^2+19w+39 equation: 


Simplifying
w2 + 10w + 25 = 2w2 + 19w + 39

Reorder the terms:
25 + 10w + w2 = 2w2 + 19w + 39

Reorder the terms:
25 + 10w + w2 = 39 + 19w + 2w2

Solving
25 + 10w + w2 = 39 + 19w + 2w2

Solving for variable 'w'.

Reorder the terms:
25 + -39 + 10w + -19w + w2 + -2w2 = 39 + 19w + 2w2 + -39 + -19w + -2w2

Combine like terms: 25 + -39 = -14
-14 + 10w + -19w + w2 + -2w2 = 39 + 19w + 2w2 + -39 + -19w + -2w2

Combine like terms: 10w + -19w = -9w
-14 + -9w + w2 + -2w2 = 39 + 19w + 2w2 + -39 + -19w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-14 + -9w + -1w2 = 39 + 19w + 2w2 + -39 + -19w + -2w2

Reorder the terms:
-14 + -9w + -1w2 = 39 + -39 + 19w + -19w + 2w2 + -2w2

Combine like terms: 39 + -39 = 0
-14 + -9w + -1w2 = 0 + 19w + -19w + 2w2 + -2w2
-14 + -9w + -1w2 = 19w + -19w + 2w2 + -2w2

Combine like terms: 19w + -19w = 0
-14 + -9w + -1w2 = 0 + 2w2 + -2w2
-14 + -9w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-14 + -9w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 9w + w2) = 0

Factor a trinomial.
-1((7 + w)(2 + w)) = 0

Ignore the factor -1.

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

Simplifying
7 + w = 0

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

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

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

Simplifying
w = -7

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 = {-7, -2}

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