-35z^2-11z+6=0

Solution for -35z^2-11z+6=0 equation:

Simplifying
-35z2 + -11z + 6 = 0

Reorder the terms:
6 + -11z + -35z2 = 0

Solving
6 + -11z + -35z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -7z)(3 + 5z) = 0

Subproblem 1
Set the factor '(2 + -7z)' equal to zero and attempt to solve:

Simplifying
2 + -7z = 0

Solving
2 + -7z = 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 + -7z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7z = 0 + -2
-7z = 0 + -2

Combine like terms: 0 + -2 = -2
-7z = -2

Divide each side by '-7'.
z = 0.2857142857

Simplifying
z = 0.2857142857
Subproblem 2
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
Solution
z = {0.2857142857, -0.6}