5z^2-13z+6=0

Solution for 5z^2-13z+6=0 equation:

Simplifying
5z2 + -13z + 6 = 0

Reorder the terms:
6 + -13z + 5z2 = 0

Solving
6 + -13z + 5z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(3 + -5z)' equal to zero and attempt to solve:

Simplifying
3 + -5z = 0

Solving
3 + -5z = 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 + -5z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5z = 0 + -3
-5z = 0 + -3

Combine like terms: 0 + -3 = -3
-5z = -3

Divide each side by '-5'.
z = 0.6

Simplifying
z = 0.6
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {0.6, 2}