4w^2+4w+1=49

Solution for 4w^2+4w+1=49 equation:

Simplifying
4w2 + 4w + 1 = 49

Reorder the terms:
1 + 4w + 4w2 = 49

Solving
1 + 4w + 4w2 = 49

Solving for variable 'w'.

Reorder the terms:
1 + -49 + 4w + 4w2 = 49 + -49

Combine like terms: 1 + -49 = -48
-48 + 4w + 4w2 = 49 + -49

Combine like terms: 49 + -49 = 0
-48 + 4w + 4w2 = 0

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

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

Ignore the factor 4.
Subproblem 1
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
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 = {-4, 3}