(2t-1)(t+3)=-6

Solution for (2t-1)(t+3)=-6 equation:

Simplifying
(2t + -1)(t + 3) = -6

Reorder the terms:
(-1 + 2t)(t + 3) = -6

Reorder the terms:
(-1 + 2t)(3 + t) = -6

Multiply (-1 + 2t) * (3 + t)
(-1(3 + t) + 2t * (3 + t)) = -6
((3 * -1 + t * -1) + 2t * (3 + t)) = -6
((-3 + -1t) + 2t * (3 + t)) = -6
(-3 + -1t + (3 * 2t + t * 2t)) = -6
(-3 + -1t + (6t + 2t2)) = -6

Combine like terms: -1t + 6t = 5t
(-3 + 5t + 2t2) = -6

Solving
-3 + 5t + 2t2 = -6

Solving for variable 't'.

Reorder the terms:
-3 + 6 + 5t + 2t2 = -6 + 6

Combine like terms: -3 + 6 = 3
3 + 5t + 2t2 = -6 + 6

Combine like terms: -6 + 6 = 0
3 + 5t + 2t2 = 0

Factor a trinomial.
(3 + 2t)(1 + t) = 0

Subproblem 1
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

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

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

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
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 = {-1.5, -1}