8z^2-18z-45=0

Solution for 8z^2-18z-45=0 equation:

Simplifying
8z2 + -18z + -45 = 0

Reorder the terms:
-45 + -18z + 8z2 = 0

Solving
-45 + -18z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -2z)(15 + -4z) = 0

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 '(15 + -4z)' equal to zero and attempt to solve:

Simplifying
15 + -4z = 0

Solving
15 + -4z = 0

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

Add '-15' to each side of the equation.
15 + -15 + -4z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4z = 0 + -15
-4z = 0 + -15

Combine like terms: 0 + -15 = -15
-4z = -15

Divide each side by '-4'.
z = 3.75

Simplifying
z = 3.75
Solution
z = {-1.5, 3.75}