6t=3(t+4)t

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

Simplifying
6t = 3(t + 4) * t

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

Reorder the terms for easier multiplication:
6t = 3t(4 + t)
6t = (4 * 3t + t * 3t)
6t = (12t + 3t2)

Solving
6t = 12t + 3t2

Solving for variable 't'.

Combine like terms: 6t + -12t = -6t
-6t + -3t2 = 12t + 3t2 + -12t + -3t2

Reorder the terms:
-6t + -3t2 = 12t + -12t + 3t2 + -3t2

Combine like terms: 12t + -12t = 0
-6t + -3t2 = 0 + 3t2 + -3t2
-6t + -3t2 = 3t2 + -3t2

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

Factor out the Greatest Common Factor (GCF), '-3t'.
-3t(2 + t) = 0

Ignore the factor -3.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

Move all terms containing t to the left, all other terms to the right.

Simplifying
t = 0
Subproblem 2
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
Solution
t = {0, -2}