t^2-2t=24+3t

Solution for t^2-2t=24+3t equation:

Simplifying
t2 + -2t = 24 + 3t

Reorder the terms:
-2t + t2 = 24 + 3t

Solving
-2t + t2 = 24 + 3t

Solving for variable 't'.

Reorder the terms:
-24 + -2t + -3t + t2 = 24 + 3t + -24 + -3t

Combine like terms: -2t + -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.
(-3 + -1t)(8 + -1t) = 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 + -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
Solution
t = {-3, 8}