2w(w+1)=w^2+15

Solution for 2w(w+1)=w^2+15 equation:

Simplifying
2w(w + 1) = w2 + 15

Reorder the terms:
2w(1 + w) = w2 + 15
(1 * 2w + w * 2w) = w2 + 15
(2w + 2w2) = w2 + 15

Reorder the terms:
2w + 2w2 = 15 + w2

Solving
2w + 2w2 = 15 + w2

Solving for variable 'w'.

Reorder the terms:
-15 + 2w + 2w2 + -1w2 = 15 + w2 + -15 + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-15 + 2w + 1w2 = 15 + w2 + -15 + -1w2

Reorder the terms:
-15 + 2w + 1w2 = 15 + -15 + w2 + -1w2

Combine like terms: 15 + -15 = 0
-15 + 2w + 1w2 = 0 + w2 + -1w2
-15 + 2w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-15 + 2w + 1w2 = 0

Factor a trinomial.
(-5 + -1w)(3 + -1w) = 0

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

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 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 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
w = -5

Simplifying
w = -5
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-5, 3}