6s^2t^2+st-1=

Solution for 6s^2t^2+st-1= equation:

Simplifying
6s2t2 + st + -1 = 0

Reorder the terms:
-1 + st + 6s2t2 = 0

Solving
-1 + st + 6s2t2 = 0

Solving for variable 's'.

Factor a trinomial.
(-1 + -2st)(1 + -3st) = 0

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

Simplifying
-1 + -2st = 0

Solving
-1 + -2st = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2st = 0 + 1

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

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

Divide each side by '-2t'.
s = -0.5t-1

Simplifying
s = -0.5t-1
Subproblem 2
Set the factor '(1 + -3st)' equal to zero and attempt to solve:

Simplifying
1 + -3st = 0

Solving
1 + -3st = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3st = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3st = 0 + -1
-3st = 0 + -1

Combine like terms: 0 + -1 = -1
-3st = -1

Divide each side by '-3t'.
s = 0.3333333333t-1

Simplifying
s = 0.3333333333t-1
Solution
s = {-0.5t-1, 0.3333333333t-1}