w^2+16=2w^2+4w+4

Solution for w^2+16=2w^2+4w+4 equation:

Simplifying
w2 + 16 = 2w2 + 4w + 4

Reorder the terms:
16 + w2 = 2w2 + 4w + 4

Reorder the terms:
16 + w2 = 4 + 4w + 2w2

Solving
16 + w2 = 4 + 4w + 2w2

Solving for variable 'w'.

Reorder the terms:
16 + -4 + -4w + w2 + -2w2 = 4 + 4w + 2w2 + -4 + -4w + -2w2

Combine like terms: 16 + -4 = 12
12 + -4w + w2 + -2w2 = 4 + 4w + 2w2 + -4 + -4w + -2w2

Combine like terms: w2 + -2w2 = -1w2
12 + -4w + -1w2 = 4 + 4w + 2w2 + -4 + -4w + -2w2

Reorder the terms:
12 + -4w + -1w2 = 4 + -4 + 4w + -4w + 2w2 + -2w2

Combine like terms: 4 + -4 = 0
12 + -4w + -1w2 = 0 + 4w + -4w + 2w2 + -2w2
12 + -4w + -1w2 = 4w + -4w + 2w2 + -2w2

Combine like terms: 4w + -4w = 0
12 + -4w + -1w2 = 0 + 2w2 + -2w2
12 + -4w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
12 + -4w + -1w2 = 0

Factor a trinomial.
(2 + -1w)(6 + w) = 0

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Subproblem 2
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
Solution
w = {2, -6}