10z^2-3z-1=0

Solution for 10z^2-3z-1=0 equation:

Simplifying
10z2 + -3z + -1 = 0

Reorder the terms:
-1 + -3z + 10z2 = 0

Solving
-1 + -3z + 10z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -5z)(1 + -2z) = 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 '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

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

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

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

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-0.2, 0.5}