3t^2+2t-5=0

Solution for 3t^2+2t-5=0 equation:

Simplifying
3t2 + 2t + -5 = 0

Reorder the terms:
-5 + 2t + 3t2 = 0

Solving
-5 + 2t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -3t)(1 + -1t) = 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 + -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 = {-1.666666667, 1}