(4t+2)(3t+6)=

Solution for (4t+2)(3t+6)= equation:

Simplifying
(4t + 2)(3t + 6) = 0

Reorder the terms:
(2 + 4t)(3t + 6) = 0

Reorder the terms:
(2 + 4t)(6 + 3t) = 0

Multiply (2 + 4t) * (6 + 3t)
(2(6 + 3t) + 4t * (6 + 3t)) = 0
((6 * 2 + 3t * 2) + 4t * (6 + 3t)) = 0
((12 + 6t) + 4t * (6 + 3t)) = 0
(12 + 6t + (6 * 4t + 3t * 4t)) = 0
(12 + 6t + (24t + 12t2)) = 0

Combine like terms: 6t + 24t = 30t
(12 + 30t + 12t2) = 0

Solving
12 + 30t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + 5t + 2t2) = 0

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

Ignore the factor 6.
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 + 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 = {-2, -0.5}