13=(t+4)(t-8)

Solution for 13=(t+4)(t-8) equation:

Simplifying
13 = (t + 4)(t + -8)

Reorder the terms:
13 = (4 + t)(t + -8)

Reorder the terms:
13 = (4 + t)(-8 + t)

Multiply (4 + t) * (-8 + t)
13 = (4(-8 + t) + t(-8 + t))
13 = ((-8 * 4 + t * 4) + t(-8 + t))
13 = ((-32 + 4t) + t(-8 + t))
13 = (-32 + 4t + (-8 * t + t * t))
13 = (-32 + 4t + (-8t + t2))

Combine like terms: 4t + -8t = -4t
13 = (-32 + -4t + t2)

Solving
13 = -32 + -4t + t2

Solving for variable 't'.

Combine like terms: 13 + 32 = 45
45 + 4t + -1t2 = -32 + -4t + t2 + 32 + 4t + -1t2

Reorder the terms:
45 + 4t + -1t2 = -32 + 32 + -4t + 4t + t2 + -1t2

Combine like terms: -32 + 32 = 0
45 + 4t + -1t2 = 0 + -4t + 4t + t2 + -1t2
45 + 4t + -1t2 = -4t + 4t + t2 + -1t2

Combine like terms: -4t + 4t = 0
45 + 4t + -1t2 = 0 + t2 + -1t2
45 + 4t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
45 + 4t + -1t2 = 0

Factor a trinomial.
(9 + -1t)(5 + t) = 0

Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 0

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

Add '-5' to each side of the equation.
5 + -5 + t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + t = 0 + -5
t = 0 + -5

Combine like terms: 0 + -5 = -5
t = -5

Simplifying
t = -5
Solution
t = {9, -5}