(3)*6t^2(t+1)=

Solution for (3)*6t^2(t+1)= equation:

Simplifying
(3) * 6t2(t + 1) = 0

Reorder the terms:
3 * 6t2(1 + t) = 0

Multiply 3 * 6
18t2(1 + t) = 0
(1 * 18t2 + t * 18t2) = 0
(18t2 + 18t3) = 0

Solving
18t2 + 18t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '18t2'.
18t2(1 + t) = 0

Ignore the factor 18.
Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
Subproblem 2
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
Solution
t = {0, -1}