72t^2-12t-24=0

Solution for 72t^2-12t-24=0 equation:

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

Reorder the terms:
-24 + -12t + 72t2 = 0

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

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-2 + -1t + 6t2) = 0

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

Ignore the factor 12.
Subproblem 1
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
Subproblem 2
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
Solution
t = {-0.5, 0.6666666667}