3(2t^2-5t-12)=0

Solution for 3(2t^2-5t-12)=0 equation:

Simplifying
3(2t2 + -5t + -12) = 0

Reorder the terms:
3(-12 + -5t + 2t2) = 0
(-12 * 3 + -5t * 3 + 2t2 * 3) = 0
(-36 + -15t + 6t2) = 0

Solving
-36 + -15t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -5t + 2t2) = 0

Factor a trinomial.
3((-3 + -2t)(4 + -1t)) = 0

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

Simplifying
-3 + -2t = 0

Solving
-3 + -2t = 0

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

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

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

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

Divide each side by '-2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-1.5, 4}