4w^2+12w+9-25=0

Solution for 4w^2+12w+9-25=0 equation:

Simplifying
4w2 + 12w + 9 + -25 = 0

Reorder the terms:
9 + -25 + 12w + 4w2 = 0

Combine like terms: 9 + -25 = -16
-16 + 12w + 4w2 = 0

Solving
-16 + 12w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 3w + w2) = 0

Factor a trinomial.
4((-4 + -1w)(1 + -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 '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Solution
w = {-4, 1}