3z(2z+9)=54

Solution for 3z(2z+9)=54 equation:

Simplifying
3z(2z + 9) = 54

Reorder the terms:
3z(9 + 2z) = 54
(9 * 3z + 2z * 3z) = 54
(27z + 6z2) = 54

Solving
27z + 6z2 = 54

Solving for variable 'z'.

Reorder the terms:
-54 + 27z + 6z2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 27z + 6z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 9z + 2z2) = 0

Factor a trinomial.
3((-6 + -1z)(3 + -2z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {-6, 1.5}