t(t-6)(t+8)=0

Solution for t(t-6)(t+8)=0 equation:

Simplifying
t(t + -6)(t + 8) = 0

Reorder the terms:
t(-6 + t)(t + 8) = 0

Reorder the terms:
t(-6 + t)(8 + t) = 0

Multiply (-6 + t) * (8 + t)
t(-6(8 + t) + t(8 + t)) = 0
t((8 * -6 + t * -6) + t(8 + t)) = 0
t((-48 + -6t) + t(8 + t)) = 0
t(-48 + -6t + (8 * t + t * t)) = 0
t(-48 + -6t + (8t + t2)) = 0

Combine like terms: -6t + 8t = 2t
t(-48 + 2t + t2) = 0
(-48 * t + 2t * t + t2 * t) = 0
(-48t + 2t2 + t3) = 0

Solving
-48t + 2t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-48 + 2t + t2) = 0

Factor a trinomial.
t((-8 + -1t)(6 + -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 '(-8 + -1t)' equal to zero and attempt to solve:

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t = 0 + 8
-1t = 0 + 8

Combine like terms: 0 + 8 = 8
-1t = 8

Divide each side by '-1'.
t = -8

Simplifying
t = -8
Subproblem 3
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {0, -8, 6}