(t+1)(2t-55)(3t)=0

Solution for (t+1)(2t-55)(3t)=0 equation:

Simplifying
(t + 1)(2t + -55)(3t) = 0

Reorder the terms:
(1 + t)(2t + -55)(3t) = 0

Reorder the terms:
(1 + t)(-55 + 2t)(3t) = 0

Remove parenthesis around (3t)
(1 + t)(-55 + 2t) * 3t = 0

Reorder the terms for easier multiplication:
3t(1 + t)(-55 + 2t) = 0

Multiply (1 + t) * (-55 + 2t)
3t(1(-55 + 2t) + t(-55 + 2t)) = 0
3t((-55 * 1 + 2t * 1) + t(-55 + 2t)) = 0
3t((-55 + 2t) + t(-55 + 2t)) = 0
3t(-55 + 2t + (-55 * t + 2t * t)) = 0
3t(-55 + 2t + (-55t + 2t2)) = 0

Combine like terms: 2t + -55t = -53t
3t(-55 + -53t + 2t2) = 0
(-55 * 3t + -53t * 3t + 2t2 * 3t) = 0
(-165t + -159t2 + 6t3) = 0

Solving
-165t + -159t2 + 6t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(-55 + -53t + 2t2) = 0

Factor a trinomial.
3t((-1 + -1t)(55 + -2t)) = 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 '(-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 '(55 + -2t)' equal to zero and attempt to solve:

Simplifying
55 + -2t = 0

Solving
55 + -2t = 0

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

Add '-55' to each side of the equation.
55 + -55 + -2t = 0 + -55

Combine like terms: 55 + -55 = 0
0 + -2t = 0 + -55
-2t = 0 + -55

Combine like terms: 0 + -55 = -55
-2t = -55

Divide each side by '-2'.
t = 27.5

Simplifying
t = 27.5
Solution
t = {0, -1, 27.5}