3t^3+2t=5t^2

Solution for 3t^3+2t=5t^2 equation:

Simplifying
3t3 + 2t = 5t2

Reorder the terms:
2t + 3t3 = 5t2

Solving
2t + 3t3 = 5t2

Solving for variable 't'.

Reorder the terms:
2t + -5t2 + 3t3 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
2t + -5t2 + 3t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(2 + -5t + 3t2) = 0

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

Simplifying
1 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {0, 0.6666666667, 1}