9z^2+54z+81=0

Solution for 9z^2+54z+81=0 equation:

Simplifying
9z2 + 54z + 81 = 0

Reorder the terms:
81 + 54z + 9z2 = 0

Solving
81 + 54z + 9z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '9'.
9(9 + 6z + z2) = 0

Factor a trinomial.
9((3 + z)(3 + z)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-3, -3}