4w^2+4w+1-25=0

Solution for 4w^2+4w+1-25=0 equation:

Simplifying
4w2 + 4w + 1 + -25 = 0

Reorder the terms:
1 + -25 + 4w + 4w2 = 0

Combine like terms: 1 + -25 = -24
-24 + 4w + 4w2 = 0

Solving
-24 + 4w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + w + w2) = 0

Factor a trinomial.
4((-3 + -1w)(2 + -1w)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-3, 2}