35z^2-2z-1=0

Solution for 35z^2-2z-1=0 equation:

Simplifying
35z2 + -2z + -1 = 0

Reorder the terms:
-1 + -2z + 35z2 = 0

Solving
-1 + -2z + 35z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -7z)(1 + -5z) = 0

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

Simplifying
-1 + -7z = 0

Solving
-1 + -7z = 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 + -7z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7z = 0 + 1
-7z = 0 + 1

Combine like terms: 0 + 1 = 1
-7z = 1

Divide each side by '-7'.
z = -0.1428571429

Simplifying
z = -0.1428571429
Subproblem 2
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
Solution
z = {-0.1428571429, 0.2}