20z^2-49z+9=0

Solution for 20z^2-49z+9=0 equation:

Simplifying
20z2 + -49z + 9 = 0

Reorder the terms:
9 + -49z + 20z2 = 0

Solving
9 + -49z + 20z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -5z)(9 + -4z) = 0

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

Simplifying
1 + -5z = 0

Solving
1 + -5z = 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 + -5z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5z = 0 + -1
-5z = 0 + -1

Combine like terms: 0 + -1 = -1
-5z = -1

Divide each side by '-5'.
z = 0.2

Simplifying
z = 0.2
Subproblem 2
Set the factor '(9 + -4z)' equal to zero and attempt to solve:

Simplifying
9 + -4z = 0

Solving
9 + -4z = 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 + -4z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4z = 0 + -9
-4z = 0 + -9

Combine like terms: 0 + -9 = -9
-4z = -9

Divide each side by '-4'.
z = 2.25

Simplifying
z = 2.25
Solution
z = {0.2, 2.25}