t^2=24-2t

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

Simplifying
t2 = 24 + -2t

Solving
t2 = 24 + -2t

Solving for variable 't'.

Reorder the terms:
-24 + 2t + t2 = 24 + -2t + -24 + 2t

Reorder the terms:
-24 + 2t + t2 = 24 + -24 + -2t + 2t

Combine like terms: 24 + -24 = 0
-24 + 2t + t2 = 0 + -2t + 2t
-24 + 2t + t2 = -2t + 2t

Combine like terms: -2t + 2t = 0
-24 + 2t + t2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
t = {-6, 4}