2w^2+7w+55=w^2+49

Solution for 2w^2+7w+55=w^2+49 equation:

Simplifying
2w2 + 7w + 55 = w2 + 49

Reorder the terms:
55 + 7w + 2w2 = w2 + 49

Reorder the terms:
55 + 7w + 2w2 = 49 + w2

Solving
55 + 7w + 2w2 = 49 + w2

Solving for variable 'w'.

Reorder the terms:
55 + -49 + 7w + 2w2 + -1w2 = 49 + w2 + -49 + -1w2

Combine like terms: 55 + -49 = 6
6 + 7w + 2w2 + -1w2 = 49 + w2 + -49 + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
6 + 7w + 1w2 = 49 + w2 + -49 + -1w2

Reorder the terms:
6 + 7w + 1w2 = 49 + -49 + w2 + -1w2

Combine like terms: 49 + -49 = 0
6 + 7w + 1w2 = 0 + w2 + -1w2
6 + 7w + 1w2 = w2 + -1w2

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

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

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

Simplifying
6 + w = 0

Solving
6 + w = 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 + w = 0 + -6

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

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

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

Simplifying
1 + w = 0

Solving
1 + w = 0

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

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

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

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

Simplifying
w = -1
Solution
w = {-6, -1}