10t^2-3t-1=0

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

Simplifying
10t2 + -3t + -1 = 0

Reorder the terms:
-1 + -3t + 10t2 = 0

Solving
-1 + -3t + 10t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(-1 + -5t)' equal to zero and attempt to solve:

Simplifying
-1 + -5t = 0

Solving
-1 + -5t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5t = 0 + 1
-5t = 0 + 1

Combine like terms: 0 + 1 = 1
-5t = 1

Divide each side by '-5'.
t = -0.2

Simplifying
t = -0.2
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

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