t+24=t(t+6)

Solution for t+24=t(t+6) equation:

Simplifying
t + 24 = t(t + 6)

Reorder the terms:
24 + t = t(t + 6)

Reorder the terms:
24 + t = t(6 + t)
24 + t = (6 * t + t * t)
24 + t = (6t + t2)

Solving
24 + t = 6t + t2

Solving for variable 't'.

Combine like terms: t + -6t = -5t
24 + -5t + -1t2 = 6t + t2 + -6t + -1t2

Reorder the terms:
24 + -5t + -1t2 = 6t + -6t + t2 + -1t2

Combine like terms: 6t + -6t = 0
24 + -5t + -1t2 = 0 + t2 + -1t2
24 + -5t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
24 + -5t + -1t2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(8 + t)' equal to zero and attempt to solve:

Simplifying
8 + t = 0

Solving
8 + t = 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 + t = 0 + -8

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

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

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