13z^2-16z+3=0

Solution for 13z^2-16z+3=0 equation:

Simplifying
13z2 + -16z + 3 = 0

Reorder the terms:
3 + -16z + 13z2 = 0

Solving
3 + -16z + 13z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -13z)(1 + -1z) = 0

Subproblem 1
Set the factor '(3 + -13z)' equal to zero and attempt to solve:

Simplifying
3 + -13z = 0

Solving
3 + -13z = 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 + -13z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -13z = 0 + -3
-13z = 0 + -3

Combine like terms: 0 + -3 = -3
-13z = -3

Divide each side by '-13'.
z = 0.2307692308

Simplifying
z = 0.2307692308
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 = {0.2307692308, 1}