(2t-8)(3+3t)=

Solution for (2t-8)(3+3t)= equation:

Simplifying
(2t + -8)(3 + 3t) = 0

Reorder the terms:
(-8 + 2t)(3 + 3t) = 0

Multiply (-8 + 2t) * (3 + 3t)
(-8(3 + 3t) + 2t * (3 + 3t)) = 0
((3 * -8 + 3t * -8) + 2t * (3 + 3t)) = 0
((-24 + -24t) + 2t * (3 + 3t)) = 0
(-24 + -24t + (3 * 2t + 3t * 2t)) = 0
(-24 + -24t + (6t + 6t2)) = 0

Combine like terms: -24t + 6t = -18t
(-24 + -18t + 6t2) = 0

Solving
-24 + -18t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -3t + t2) = 0

Factor a trinomial.
6((-1 + -1t)(4 + -1t)) = 0

Ignore the factor 6.
Subproblem 1
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 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-1, 4}