112=23t-t^2

Solution for 112=23t-t^2 equation:

Simplifying
112 = 23t + -1t2

Solving
112 = 23t + -1t2

Solving for variable 't'.

Reorder the terms:
112 + -23t + t2 = 23t + -23t + -1t2 + t2

Combine like terms: 23t + -23t = 0
112 + -23t + t2 = 0 + -1t2 + t2
112 + -23t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
112 + -23t + t2 = 0

Factor a trinomial.
(7 + -1t)(16 + -1t) = 0

Subproblem 1
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Subproblem 2
Set the factor '(16 + -1t)' equal to zero and attempt to solve:

Simplifying
16 + -1t = 0

Solving
16 + -1t = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1t = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1t = 0 + -16
-1t = 0 + -16

Combine like terms: 0 + -16 = -16
-1t = -16

Divide each side by '-1'.
t = 16

Simplifying
t = 16
Solution
t = {7, 16}