2(24w+2w^2)+2(16w)=276

Solution for 2(24w+2w^2)+2(16w)=276 equation:

Simplifying
2(24w + 2w2) + 2(16w) = 276
(24w * 2 + 2w2 * 2) + 2(16w) = 276
(48w + 4w2) + 2(16w) = 276

Remove parenthesis around (16w)
48w + 4w2 + 2 * 16w = 276

Multiply 2 * 16
48w + 4w2 + 32w = 276

Reorder the terms:
48w + 32w + 4w2 = 276

Combine like terms: 48w + 32w = 80w
80w + 4w2 = 276

Solving
80w + 4w2 = 276

Solving for variable 'w'.

Reorder the terms:
-276 + 80w + 4w2 = 276 + -276

Combine like terms: 276 + -276 = 0
-276 + 80w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-69 + 20w + w2) = 0

Factor a trinomial.
4((-23 + -1w)(3 + -1w)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-23 + -1w)' equal to zero and attempt to solve:

Simplifying
-23 + -1w = 0

Solving
-23 + -1w = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1w = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1w = 0 + 23
-1w = 0 + 23

Combine like terms: 0 + 23 = 23
-1w = 23

Divide each side by '-1'.
w = -23

Simplifying
w = -23
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 = {-23, 3}