21=10t-t^2

Solution for 21=10t-t^2 equation:

Simplifying
21 = 10t + -1t2

Solving
21 = 10t + -1t2

Solving for variable 't'.

Reorder the terms:
21 + -10t + t2 = 10t + -10t + -1t2 + t2

Combine like terms: 10t + -10t = 0
21 + -10t + t2 = 0 + -1t2 + t2
21 + -10t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
21 + -10t + t2 = 0

Factor a trinomial.
(3 + -1t)(7 + -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 '(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
Solution
t = {3, 7}