(3t-2)(t+4)=-15

Solution for (3t-2)(t+4)=-15 equation:

Simplifying
(3t + -2)(t + 4) = -15

Reorder the terms:
(-2 + 3t)(t + 4) = -15

Reorder the terms:
(-2 + 3t)(4 + t) = -15

Multiply (-2 + 3t) * (4 + t)
(-2(4 + t) + 3t * (4 + t)) = -15
((4 * -2 + t * -2) + 3t * (4 + t)) = -15
((-8 + -2t) + 3t * (4 + t)) = -15
(-8 + -2t + (4 * 3t + t * 3t)) = -15
(-8 + -2t + (12t + 3t2)) = -15

Combine like terms: -2t + 12t = 10t
(-8 + 10t + 3t2) = -15

Solving
-8 + 10t + 3t2 = -15

Solving for variable 't'.

Reorder the terms:
-8 + 15 + 10t + 3t2 = -15 + 15

Combine like terms: -8 + 15 = 7
7 + 10t + 3t2 = -15 + 15

Combine like terms: -15 + 15 = 0
7 + 10t + 3t2 = 0

Factor a trinomial.
(7 + 3t)(1 + t) = 0

Subproblem 1
Set the factor '(7 + 3t)' equal to zero and attempt to solve:

Simplifying
7 + 3t = 0

Solving
7 + 3t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3t = 0 + -7
3t = 0 + -7

Combine like terms: 0 + -7 = -7
3t = -7

Divide each side by '3'.
t = -2.333333333

Simplifying
t = -2.333333333
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 = {-2.333333333, -1}