3z(2z+11)=18

Solution for 3z(2z+11)=18 equation:

Simplifying
3z(2z + 11) = 18

Reorder the terms:
3z(11 + 2z) = 18
(11 * 3z + 2z * 3z) = 18
(33z + 6z2) = 18

Solving
33z + 6z2 = 18

Solving for variable 'z'.

Reorder the terms:
-18 + 33z + 6z2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 33z + 6z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 11z + 2z2) = 0

Factor a trinomial.
3((-6 + -1z)(1 + -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 '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

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

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

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

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-6, 0.5}