w(w+1)=12

Solution for w(w+1)=12 equation:

Simplifying
w(w + 1) = 12

Reorder the terms:
w(1 + w) = 12
(1 * w + w * w) = 12
(1w + w2) = 12

Solving
1w + w2 = 12

Solving for variable 'w'.

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

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

Factor a trinomial.
(-4 + -1w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1w = 0 + 4

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

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

Divide each side by '-1'.
w = -4

Simplifying
w = -4
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 = {-4, 3}