4w^2+12w+9=81

Solution for 4w^2+12w+9=81 equation:

Simplifying
4w2 + 12w + 9 = 81

Reorder the terms:
9 + 12w + 4w2 = 81

Solving
9 + 12w + 4w2 = 81

Solving for variable 'w'.

Reorder the terms:
9 + -81 + 12w + 4w2 = 81 + -81

Combine like terms: 9 + -81 = -72
-72 + 12w + 4w2 = 81 + -81

Combine like terms: 81 + -81 = 0
-72 + 12w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 3w + w2) = 0

Factor a trinomial.
4((-6 + -1w)(3 + -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 '(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 = {-6, 3}