-44t^4+51t^3+5t^2=0

Solution for -44t^4+51t^3+5t^2=0 equation:

Simplifying
-44t4 + 51t3 + 5t2 = 0

Reorder the terms:
5t2 + 51t3 + -44t4 = 0

Solving
5t2 + 51t3 + -44t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't2'.
t2(5 + 51t + -44t2) = 0

Factor a trinomial.
t2((5 + -4t)(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 '(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 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, 1.25, -0.09090909091}