(2t+1)(t+1)-2(t+1)=0

Solution for (2t+1)(t+1)-2(t+1)=0 equation:

Simplifying
(2t + 1)(t + 1) + -2(t + 1) = 0

Reorder the terms:
(1 + 2t)(t + 1) + -2(t + 1) = 0

Reorder the terms:
(1 + 2t)(1 + t) + -2(t + 1) = 0

Multiply (1 + 2t) * (1 + t)
(1(1 + t) + 2t * (1 + t)) + -2(t + 1) = 0
((1 * 1 + t * 1) + 2t * (1 + t)) + -2(t + 1) = 0
((1 + 1t) + 2t * (1 + t)) + -2(t + 1) = 0
(1 + 1t + (1 * 2t + t * 2t)) + -2(t + 1) = 0
(1 + 1t + (2t + 2t2)) + -2(t + 1) = 0

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

Reorder the terms:
1 + 3t + 2t2 + -2(1 + t) = 0
1 + 3t + 2t2 + (1 * -2 + t * -2) = 0
1 + 3t + 2t2 + (-2 + -2t) = 0

Reorder the terms:
1 + -2 + 3t + -2t + 2t2 = 0

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

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

Solving
-1 + 1t + 2t2 = 0

Solving for variable 't'.

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

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

Simplifying
-1 + -1t = 0

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

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

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

Divide each side by '-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}