0=10z^2+27z+18

Solution for 0=10z^2+27z+18 equation:

Simplifying
0 = 10z2 + 27z + 18

Reorder the terms:
0 = 18 + 27z + 10z2

Solving
0 = 18 + 27z + 10z2

Solving for variable 'z'.

Combine like terms: 0 + -18 = -18
-18 + -27z + -10z2 = 18 + 27z + 10z2 + -18 + -27z + -10z2

Reorder the terms:
-18 + -27z + -10z2 = 18 + -18 + 27z + -27z + 10z2 + -10z2

Combine like terms: 18 + -18 = 0
-18 + -27z + -10z2 = 0 + 27z + -27z + 10z2 + -10z2
-18 + -27z + -10z2 = 27z + -27z + 10z2 + -10z2

Combine like terms: 27z + -27z = 0
-18 + -27z + -10z2 = 0 + 10z2 + -10z2
-18 + -27z + -10z2 = 10z2 + -10z2

Combine like terms: 10z2 + -10z2 = 0
-18 + -27z + -10z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 27z + 10z2) = 0

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

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + 5z)' equal to zero and attempt to solve:

Simplifying
6 + 5z = 0

Solving
6 + 5z = 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 + 5z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5z = 0 + -6
5z = 0 + -6

Combine like terms: 0 + -6 = -6
5z = -6

Divide each side by '5'.
z = -1.2

Simplifying
z = -1.2
Solution
z = {-1.5, -1.2}