4w^2+4w+1=121

Solution for 4w^2+4w+1=121 equation:

Simplifying
4w2 + 4w + 1 = 121

Reorder the terms:
1 + 4w + 4w2 = 121

Solving
1 + 4w + 4w2 = 121

Solving for variable 'w'.

Reorder the terms:
1 + -121 + 4w + 4w2 = 121 + -121

Combine like terms: 1 + -121 = -120
-120 + 4w + 4w2 = 121 + -121

Combine like terms: 121 + -121 = 0
-120 + 4w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + w + w2) = 0

Factor a trinomial.
4((-6 + -1w)(5 + -1w)) = 0

Ignore the factor 4.
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 '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-6, 5}