-33t^4+19t^3+2t^2=0

Solution for -33t^4+19t^3+2t^2=0 equation:

Simplifying
-33t4 + 19t3 + 2t2 = 0

Reorder the terms:
2t2 + 19t3 + -33t4 = 0

Solving
2t2 + 19t3 + -33t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't2'.
t2(2 + 19t + -33t2) = 0

Factor a trinomial.
t2((2 + -3t)(1 + 11t)) = 0

Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
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
Subproblem 3
Set the factor '(1 + 11t)' equal to zero and attempt to solve:

Simplifying
1 + 11t = 0

Solving
1 + 11t = 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 + 11t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 11t = 0 + -1
11t = 0 + -1

Combine like terms: 0 + -1 = -1
11t = -1

Divide each side by '11'.
t = -0.09090909091

Simplifying
t = -0.09090909091
Solution
t = {0, 0.6666666667, -0.09090909091}