6t^3=t^2+t

Solution for 6t^3=t^2+t equation:

Simplifying
6t3 = t2 + t

Reorder the terms:
6t3 = t + t2

Solving
6t3 = t + t2

Solving for variable 't'.

Reorder the terms:
-1t + -1t2 + 6t3 = t + t2 + -1t + -1t2

Reorder the terms:
-1t + -1t2 + 6t3 = t + -1t + t2 + -1t2

Combine like terms: t + -1t = 0
-1t + -1t2 + 6t3 = 0 + t2 + -1t2
-1t + -1t2 + 6t3 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-1t + -1t2 + 6t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-1 + -1t + 6t2) = 0

Factor a trinomial.
t((-1 + -3t)(1 + -2t)) = 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 '(-1 + -3t)' equal to zero and attempt to solve:

Simplifying
-1 + -3t = 0

Solving
-1 + -3t = 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 + -3t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3t = 0 + 1
-3t = 0 + 1

Combine like terms: 0 + 1 = 1
-3t = 1

Divide each side by '-3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Subproblem 3
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {0, -0.3333333333, 0.5}