2t=3t^2-5

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

Simplifying
2t = 3t2 + -5

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

Solving
2t = -5 + 3t2

Solving for variable 't'.

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

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

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

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

Factor a trinomial.
(5 + -3t)(1 + t) = 0

Subproblem 1
Set the factor '(5 + -3t)' equal to zero and attempt to solve:

Simplifying
5 + -3t = 0

Solving
5 + -3t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3t = 0 + -5
-3t = 0 + -5

Combine like terms: 0 + -5 = -5
-3t = -5

Divide each side by '-3'.
t = 1.666666667

Simplifying
t = 1.666666667
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

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

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

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

Simplifying
t = -1
Solution
t = {1.666666667, -1}