2t^3+6t=8t^2

Solution for 2t^3+6t=8t^2 equation:

Simplifying
2t3 + 6t = 8t2

Reorder the terms:
6t + 2t3 = 8t2

Solving
6t + 2t3 = 8t2

Solving for variable 't'.

Reorder the terms:
6t + -8t2 + 2t3 = 8t2 + -8t2

Combine like terms: 8t2 + -8t2 = 0
6t + -8t2 + 2t3 = 0

Factor out the Greatest Common Factor (GCF), '2t'.
2t(3 + -4t + t2) = 0

Factor a trinomial.
2t((1 + -1t)(3 + -1t)) = 0

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {0, 1, 3}