3t^2+t-4=0

Solution for 3t^2+t-4=0 equation:

Simplifying
3t2 + t + -4 = 0

Reorder the terms:
-4 + t + 3t2 = 0

Solving
-4 + t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-4 + -3t)(1 + -1t) = 0

Subproblem 1
Set the factor '(-4 + -3t)' equal to zero and attempt to solve:

Simplifying
-4 + -3t = 0

Solving
-4 + -3t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3t = 0 + 4
-3t = 0 + 4

Combine like terms: 0 + 4 = 4
-3t = 4

Divide each side by '-3'.
t = -1.333333333

Simplifying
t = -1.333333333
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 = {-1.333333333, 1}