2w(w+1)=w^2+3

Solution for 2w(w+1)=w^2+3 equation:

Simplifying
2w(w + 1) = w2 + 3

Reorder the terms:
2w(1 + w) = w2 + 3
(1 * 2w + w * 2w) = w2 + 3
(2w + 2w2) = w2 + 3

Reorder the terms:
2w + 2w2 = 3 + w2

Solving
2w + 2w2 = 3 + w2

Solving for variable 'w'.

Reorder the terms:
-3 + 2w + 2w2 + -1w2 = 3 + w2 + -3 + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-3 + 2w + 1w2 = 3 + w2 + -3 + -1w2

Reorder the terms:
-3 + 2w + 1w2 = 3 + -3 + w2 + -1w2

Combine like terms: 3 + -3 = 0
-3 + 2w + 1w2 = 0 + w2 + -1w2
-3 + 2w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-3 + 2w + 1w2 = 0

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

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

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Solution
w = {-3, 1}