12t^2-5t-25=0

Solution for 12t^2-5t-25=0 equation:

Simplifying
12t2 + -5t + -25 = 0

Reorder the terms:
-25 + -5t + 12t2 = 0

Solving
-25 + -5t + 12t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -4t)(5 + -3t) = 0

Subproblem 1
Set the factor '(-5 + -4t)' equal to zero and attempt to solve:

Simplifying
-5 + -4t = 0

Solving
-5 + -4t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4t = 0 + 5
-4t = 0 + 5

Combine like terms: 0 + 5 = 5
-4t = 5

Divide each side by '-4'.
t = -1.25

Simplifying
t = -1.25
Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve:

Simplifying
5 + -3t = 0

Solving
5 + -3t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3t = 0 + -5
-3t = 0 + -5

Combine like terms: 0 + -5 = -5
-3t = -5

Divide each side by '-3'.
t = 1.666666667

Simplifying
t = 1.666666667
Solution
t = {-1.25, 1.666666667}