3z^2+42z+135=0

Solution for 3z^2+42z+135=0 equation:

Simplifying
3z2 + 42z + 135 = 0

Reorder the terms:
135 + 42z + 3z2 = 0

Solving
135 + 42z + 3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(45 + 14z + z2) = 0

Factor a trinomial.
3((9 + z)(5 + z)) = 0

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

Simplifying
9 + z = 0

Solving
9 + z = 0

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

Add '-9' to each side of the equation.
9 + -9 + z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + z = 0 + -9
z = 0 + -9

Combine like terms: 0 + -9 = -9
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 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 + z = 0 + -5

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

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

Simplifying
z = -5
Solution
z = {-9, -5}