3(6z(2z+5)+(2z+5))=0

Solution for 3(6z(2z+5)+(2z+5))=0 equation:

Simplifying
3(6z(2z + 5) + (2z + 5)) = 0

Reorder the terms:
3(6z(5 + 2z) + (2z + 5)) = 0
3((5 * 6z + 2z * 6z) + (2z + 5)) = 0
3((30z + 12z2) + (2z + 5)) = 0

Reorder the terms:
3(30z + 12z2 + (5 + 2z)) = 0

Remove parenthesis around (5 + 2z)
3(30z + 12z2 + 5 + 2z) = 0

Reorder the terms:
3(5 + 30z + 2z + 12z2) = 0

Combine like terms: 30z + 2z = 32z
3(5 + 32z + 12z2) = 0
(5 * 3 + 32z * 3 + 12z2 * 3) = 0
(15 + 96z + 36z2) = 0

Solving
15 + 96z + 36z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 32z + 12z2) = 0

Factor a trinomial.
3((5 + 2z)(1 + 6z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 2z)' equal to zero and attempt to solve:

Simplifying
5 + 2z = 0

Solving
5 + 2z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2z = 0 + -5
2z = 0 + -5

Combine like terms: 0 + -5 = -5
2z = -5

Divide each side by '2'.
z = -2.5

Simplifying
z = -2.5
Subproblem 2
Set the factor '(1 + 6z)' equal to zero and attempt to solve:

Simplifying
1 + 6z = 0

Solving
1 + 6z = 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 + 6z = 0 + -1

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

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

Divide each side by '6'.
z = -0.1666666667

Simplifying
z = -0.1666666667
Solution
z = {-2.5, -0.1666666667}