3t^2+7t+4=0

Solution for 3t^2+7t+4=0 equation:

Simplifying
3t2 + 7t + 4 = 0

Reorder the terms:
4 + 7t + 3t2 = 0

Solving
4 + 7t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(4 + 3t)(1 + t) = 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 + 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 = {-1.333333333, -1}