48t^2-90t-12=0

Solution for 48t^2-90t-12=0 equation:

Simplifying
48t2 + -90t + -12 = 0

Reorder the terms:
-12 + -90t + 48t2 = 0

Solving
-12 + -90t + 48t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -15t + 8t2) = 0

Factor a trinomial.
6((-1 + -8t)(2 + -1t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -8t)' equal to zero and attempt to solve:

Simplifying
-1 + -8t = 0

Solving
-1 + -8t = 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 + -8t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8t = 0 + 1
-8t = 0 + 1

Combine like terms: 0 + 1 = 1
-8t = 1

Divide each side by '-8'.
t = -0.125

Simplifying
t = -0.125
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-0.125, 2}