3t^2+23t+40=0

Solution for 3t^2+23t+40=0 equation:

Simplifying
3t2 + 23t + 40 = 0

Reorder the terms:
40 + 23t + 3t2 = 0

Solving
40 + 23t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(5 + t)(8 + 3t) = 0

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

Simplifying
5 + t = 0

Solving
5 + t = 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 + t = 0 + -5

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

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

Simplifying
t = -5
Subproblem 2
Set the factor '(8 + 3t)' equal to zero and attempt to solve:

Simplifying
8 + 3t = 0

Solving
8 + 3t = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3t = 0 + -8
3t = 0 + -8

Combine like terms: 0 + -8 = -8
3t = -8

Divide each side by '3'.
t = -2.666666667

Simplifying
t = -2.666666667
Solution
t = {-5, -2.666666667}