(3t-1)(t+4)=-10

Solution for (3t-1)(t+4)=-10 equation:

Simplifying
(3t + -1)(t + 4) = -10

Reorder the terms:
(-1 + 3t)(t + 4) = -10

Reorder the terms:
(-1 + 3t)(4 + t) = -10

Multiply (-1 + 3t) * (4 + t)
(-1(4 + t) + 3t * (4 + t)) = -10
((4 * -1 + t * -1) + 3t * (4 + t)) = -10
((-4 + -1t) + 3t * (4 + t)) = -10
(-4 + -1t + (4 * 3t + t * 3t)) = -10
(-4 + -1t + (12t + 3t2)) = -10

Combine like terms: -1t + 12t = 11t
(-4 + 11t + 3t2) = -10

Solving
-4 + 11t + 3t2 = -10

Solving for variable 't'.

Reorder the terms:
-4 + 10 + 11t + 3t2 = -10 + 10

Combine like terms: -4 + 10 = 6
6 + 11t + 3t2 = -10 + 10

Combine like terms: -10 + 10 = 0
6 + 11t + 3t2 = 0

Factor a trinomial.
(3 + t)(2 + 3t) = 0

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

Simplifying
3 + t = 0

Solving
3 + t = 0

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

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

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

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

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

Simplifying
2 + 3t = 0

Solving
2 + 3t = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3t = 0 + -2

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

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

Divide each side by '3'.
t = -0.6666666667

Simplifying
t = -0.6666666667
Solution
t = {-3, -0.6666666667}