4w^2+4w+1=169

Solution for 4w^2+4w+1=169 equation:

Simplifying
4w2 + 4w + 1 = 169

Reorder the terms:
1 + 4w + 4w2 = 169

Solving
1 + 4w + 4w2 = 169

Solving for variable 'w'.

Reorder the terms:
1 + -169 + 4w + 4w2 = 169 + -169

Combine like terms: 1 + -169 = -168
-168 + 4w + 4w2 = 169 + -169

Combine like terms: 169 + -169 = 0
-168 + 4w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-42 + w + w2) = 0

Factor a trinomial.
4((-7 + -1w)(6 + -1w)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve:

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7
Subproblem 2
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
Solution
w = {-7, 6}