t^2=10t-24

Solution for t^2=10t-24 equation:

Simplifying
t2 = 10t + -24

Reorder the terms:
t2 = -24 + 10t

Solving
t2 = -24 + 10t

Solving for variable 't'.

Reorder the terms:
24 + -10t + t2 = -24 + 10t + 24 + -10t

Reorder the terms:
24 + -10t + t2 = -24 + 24 + 10t + -10t

Combine like terms: -24 + 24 = 0
24 + -10t + t2 = 0 + 10t + -10t
24 + -10t + t2 = 10t + -10t

Combine like terms: 10t + -10t = 0
24 + -10t + t2 = 0

Factor a trinomial.
(4 + -1t)(6 + -1t) = 0

Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {4, 6}