-20t^4+48t^3+5t^2=

Solution for -20t^4+48t^3+5t^2= equation:

Simplifying
-20t4 + 48t3 + 5t2 = 0

Reorder the terms:
5t2 + 48t3 + -20t4 = 0

Solving
5t2 + 48t3 + -20t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't2'.
t2(5 + 48t + -20t2) = 0

Factor a trinomial.
t2((5 + -2t)(1 + 10t)) = 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 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 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 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Subproblem 3
Set the factor '(1 + 10t)' equal to zero and attempt to solve:

Simplifying
1 + 10t = 0

Solving
1 + 10t = 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 + 10t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10t = 0 + -1
10t = 0 + -1

Combine like terms: 0 + -1 = -1
10t = -1

Divide each side by '10'.
t = -0.1

Simplifying
t = -0.1
Solution
t = {0, 2.5, -0.1}