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

Solution for (t+8)(t-3)=0 equation:

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

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

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

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

Combine like terms: 8t + -3t = 5t
(-24 + 5t + t2) = 0

Solving
-24 + 5t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-8 + -1t)(3 + -1t) = 0

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-8, 3}