24=t(t-5)

Solution for 24=t(t-5) equation:

Simplifying
24 = t(t + -5)

Reorder the terms:
24 = t(-5 + t)
24 = (-5 * t + t * t)
24 = (-5t + t2)

Solving
24 = -5t + t2

Solving for variable 't'.

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

Combine like terms: -5t + 5t = 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.
(8 + -1t)(3 + t) = 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 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

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