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

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

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

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

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

Multiply (5 + 2z) * (2 + z)
3(5(2 + z) + 2z * (2 + z)) = 0
3((2 * 5 + z * 5) + 2z * (2 + z)) = 0
3((10 + 5z) + 2z * (2 + z)) = 0
3(10 + 5z + (2 * 2z + z * 2z)) = 0
3(10 + 5z + (4z + 2z2)) = 0

Combine like terms: 5z + 4z = 9z
3(10 + 9z + 2z2) = 0
(10 * 3 + 9z * 3 + 2z2 * 3) = 0
(30 + 27z + 6z2) = 0

Solving
30 + 27z + 6z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 9z + 2z2) = 0

Factor a trinomial.
3((5 + 2z)(2 + z)) = 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 '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 0

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

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

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

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

Simplifying
z = -2
Solution
z = {-2.5, -2}