t(8+t)=3(t+8)

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

Simplifying
t(8 + t) = 3(t + 8)
(8 * t + t * t) = 3(t + 8)
(8t + t2) = 3(t + 8)

Reorder the terms:
8t + t2 = 3(8 + t)
8t + t2 = (8 * 3 + t * 3)
8t + t2 = (24 + 3t)

Solving
8t + t2 = 24 + 3t

Solving for variable 't'.

Reorder the terms:
-24 + 8t + -3t + t2 = 24 + 3t + -24 + -3t

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

Reorder the terms:
-24 + 5t + t2 = 24 + -24 + 3t + -3t

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

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

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}