w+w+w+w=w^2+3

Solution for w+w+w+w=w^2+3 equation:

Simplifying
w + w + w + w = w2 + 3

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

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

Combine like terms: 3w + w = 4w
4w = w2 + 3

Reorder the terms:
4w = 3 + w2

Solving
4w = 3 + w2

Solving for variable 'w'.

Reorder the terms:
-3 + 4w + -1w2 = 3 + w2 + -3 + -1w2

Reorder the terms:
-3 + 4w + -1w2 = 3 + -3 + w2 + -1w2

Combine like terms: 3 + -3 = 0
-3 + 4w + -1w2 = 0 + w2 + -1w2
-3 + 4w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-3 + 4w + -1w2 = 0

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

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

Simplifying
-3 + w = 0

Solving
-3 + w = 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 + w = 0 + 3

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

Combine like terms: 0 + 3 = 3
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}