5z^2+4z-9=0

Solution for 5z^2+4z-9=0 equation:

Simplifying
5z2 + 4z + -9 = 0

Reorder the terms:
-9 + 4z + 5z2 = 0

Solving
-9 + 4z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -5z)(1 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -5z)' equal to zero and attempt to solve:

Simplifying
-9 + -5z = 0

Solving
-9 + -5z = 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 + -5z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5z = 0 + 9
-5z = 0 + 9

Combine like terms: 0 + 9 = 9
-5z = 9

Divide each side by '-5'.
z = -1.8

Simplifying
z = -1.8
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

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

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

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

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {-1.8, 1}