0=12(6t^2-t-2)

Solution for 0=12(6t^2-t-2) equation:

Simplifying
0 = 12(6t2 + -1t + -2)

Reorder the terms:
0 = 12(-2 + -1t + 6t2)
0 = (-2 * 12 + -1t * 12 + 6t2 * 12)
0 = (-24 + -12t + 72t2)

Solving
0 = -24 + -12t + 72t2

Solving for variable 't'.

Combine like terms: 0 + 24 = 24
24 + 12t + -72t2 = -24 + -12t + 72t2 + 24 + 12t + -72t2

Reorder the terms:
24 + 12t + -72t2 = -24 + 24 + -12t + 12t + 72t2 + -72t2

Combine like terms: -24 + 24 = 0
24 + 12t + -72t2 = 0 + -12t + 12t + 72t2 + -72t2
24 + 12t + -72t2 = -12t + 12t + 72t2 + -72t2

Combine like terms: -12t + 12t = 0
24 + 12t + -72t2 = 0 + 72t2 + -72t2
24 + 12t + -72t2 = 72t2 + -72t2

Combine like terms: 72t2 + -72t2 = 0
24 + 12t + -72t2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(2 + t + -6t2) = 0

Factor a trinomial.
12((2 + -3t)(1 + 2t)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(2 + -3t)' equal to zero and attempt to solve:

Simplifying
2 + -3t = 0

Solving
2 + -3t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
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 = {0.6666666667, -0.5}