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

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

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

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

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

Multiply (-1 + 2t) * (2 + t)
(-1(2 + t) + 2t * (2 + t)) = -3
((2 * -1 + t * -1) + 2t * (2 + t)) = -3
((-2 + -1t) + 2t * (2 + t)) = -3
(-2 + -1t + (2 * 2t + t * 2t)) = -3
(-2 + -1t + (4t + 2t2)) = -3

Combine like terms: -1t + 4t = 3t
(-2 + 3t + 2t2) = -3

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

Solving for variable 't'.

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

Combine like terms: -2 + 3 = 1
1 + 3t + 2t2 = -3 + 3

Combine like terms: -3 + 3 = 0
1 + 3t + 2t2 = 0

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

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

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-1, -0.5}