2w(w+2)=w^2+12

Solution for 2w(w+2)=w^2+12 equation:

Simplifying
2w(w + 2) = w2 + 12

Reorder the terms:
2w(2 + w) = w2 + 12
(2 * 2w + w * 2w) = w2 + 12
(4w + 2w2) = w2 + 12

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

Solving
4w + 2w2 = 12 + w2

Solving for variable 'w'.

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

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

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

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

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

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

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

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 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 + -1w = 0 + 6

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

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

Divide each side by '-1'.
w = -6

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