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

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

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

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

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

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

Combine like terms: 1t + -2t = -1t
t(-2 + -1t + t2) = 0
(-2 * t + -1t * t + t2 * t) = 0
(-2t + -1t2 + t3) = 0

Solving
-2t + -1t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-2 + -1t + t2) = 0

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

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 '(-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 3
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0, -1, 2}