t^2(15t-2)=8t

Solution for t^2(15t-2)=8t equation:

Simplifying
t2(15t + -2) = 8t

Reorder the terms:
t2(-2 + 15t) = 8t
(-2 * t2 + 15t * t2) = 8t
(-2t2 + 15t3) = 8t

Solving
-2t2 + 15t3 = 8t

Solving for variable 't'.

Reorder the terms:
-8t + -2t2 + 15t3 = 8t + -8t

Combine like terms: 8t + -8t = 0
-8t + -2t2 + 15t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-8 + -2t + 15t2) = 0

Factor a trinomial.
t((-2 + -3t)(4 + -5t)) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
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 '(4 + -5t)' equal to zero and attempt to solve:

Simplifying
4 + -5t = 0

Solving
4 + -5t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5t = 0 + -4
-5t = 0 + -4

Combine like terms: 0 + -4 = -4
-5t = -4

Divide each side by '-5'.
t = 0.8

Simplifying
t = 0.8
Solution
t = {0, -0.6666666667, 0.8}