48w^2+48w+12=0

Solution for 48w^2+48w+12=0 equation:

Simplifying
48w2 + 48w + 12 = 0

Reorder the terms:
12 + 48w + 48w2 = 0

Solving
12 + 48w + 48w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '12'.
12(1 + 4w + 4w2) = 0

Factor a trinomial.
12((1 + 2w)(1 + 2w)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 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 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 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 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {-0.5, -0.5}