3t^2-10t-32=0

Solution for 3t^2-10t-32=0 equation:

Simplifying
3t2 + -10t + -32 = 0

Reorder the terms:
-32 + -10t + 3t2 = 0

Solving
-32 + -10t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-2 + -1t)(16 + -3t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(16 + -3t)' equal to zero and attempt to solve:

Simplifying
16 + -3t = 0

Solving
16 + -3t = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3t = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3t = 0 + -16
-3t = 0 + -16

Combine like terms: 0 + -16 = -16
-3t = -16

Divide each side by '-3'.
t = 5.333333333

Simplifying
t = 5.333333333
Solution
t = {-2, 5.333333333}