(2+w)(w)=24

Solution for (2+w)(w)=24 equation:

Simplifying
(2 + w)(w) = 24

Reorder the terms for easier multiplication:
w(2 + w) = 24
(2 * w + w * w) = 24
(2w + w2) = 24

Solving
2w + w2 = 24

Solving for variable 'w'.

Reorder the terms:
-24 + 2w + w2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 2w + w2 = 0

Factor a trinomial.
(-6 + -1w)(4 + -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 '(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
Solution
w = {-6, 4}