32=48t^2-16t

Solution for 32=48t^2-16t equation:

Simplifying
32 = 48t2 + -16t

Reorder the terms:
32 = -16t + 48t2

Solving
32 = -16t + 48t2

Solving for variable 't'.

Reorder the terms:
32 + 16t + -48t2 = -16t + 16t + 48t2 + -48t2

Combine like terms: -16t + 16t = 0
32 + 16t + -48t2 = 0 + 48t2 + -48t2
32 + 16t + -48t2 = 48t2 + -48t2

Combine like terms: 48t2 + -48t2 = 0
32 + 16t + -48t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(2 + t + -3t2) = 0

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
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 = {1, -0.6666666667}