-t(5t^2+t)=

Solution for -t(5t^2+t)= equation:

Simplifying
-1t(5t2 + t) = 0

Reorder the terms:
-1t(t + 5t2) = 0
(t * -1t + 5t2 * -1t) = 0
(-1t2 + -5t3) = 0

Solving
-1t2 + -5t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1t2'.
-1t2(1 + 5t) = 0

Ignore the factor -1.
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 '(1 + 5t)' equal to zero and attempt to solve:

Simplifying
1 + 5t = 0

Solving
1 + 5t = 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 + 5t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5t = 0 + -1
5t = 0 + -1

Combine like terms: 0 + -1 = -1
5t = -1

Divide each side by '5'.
t = -0.2

Simplifying
t = -0.2
Solution
t = {0, -0.2}