(6X^2)+X-1=0

Solution for (6X^2)+X-1=0 equation:

Simplifying
(6X2) + X + -1 = 0

Reorder the terms:
-1 + X + (6X2) = 0

Solving
-1 + X + (6X2) = 0

Solving for variable 'X'.

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

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

Simplifying
-1 + -2X = 0

Solving
-1 + -2X = 0

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

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

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

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

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

Simplifying
X = -0.5
Subproblem 2
Set the factor '(1 + -3X)' equal to zero and attempt to solve:

Simplifying
1 + -3X = 0

Solving
1 + -3X = 0

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

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

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

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

Divide each side by '-3'.
X = 0.3333333333

Simplifying
X = 0.3333333333
Solution
X = {-0.5, 0.3333333333}