w(w+4)=12

Solution for w(w+4)=12 equation:

Simplifying
w(w + 4) = 12

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

Solving
4w + w2 = 12

Solving for variable 'w'.

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

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