(t+2)(6t+1)=0

Solution for (t+2)(6t+1)=0 equation:

Simplifying
(t + 2)(6t + 1) = 0

Reorder the terms:
(2 + t)(6t + 1) = 0

Reorder the terms:
(2 + t)(1 + 6t) = 0

Multiply (2 + t) * (1 + 6t)
(2(1 + 6t) + t(1 + 6t)) = 0
((1 * 2 + 6t * 2) + t(1 + 6t)) = 0
((2 + 12t) + t(1 + 6t)) = 0
(2 + 12t + (1 * t + 6t * t)) = 0
(2 + 12t + (1t + 6t2)) = 0

Combine like terms: 12t + 1t = 13t
(2 + 13t + 6t2) = 0

Solving
2 + 13t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + t)(1 + 6t) = 0

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

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Subproblem 2
Set the factor '(1 + 6t)' equal to zero and attempt to solve:

Simplifying
1 + 6t = 0

Solving
1 + 6t = 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 + 6t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6t = 0 + -1
6t = 0 + -1

Combine like terms: 0 + -1 = -1
6t = -1

Divide each side by '6'.
t = -0.1666666667

Simplifying
t = -0.1666666667
Solution
t = {-2, -0.1666666667}