10=7t-t^2

Solution for 10=7t-t^2 equation:

Simplifying
10 = 7t + -1t2

Solving
10 = 7t + -1t2

Solving for variable 't'.

Reorder the terms:
10 + -7t + t2 = 7t + -7t + -1t2 + t2

Combine like terms: 7t + -7t = 0
10 + -7t + t2 = 0 + -1t2 + t2
10 + -7t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
10 + -7t + t2 = 0

Factor a trinomial.
(2 + -1t)(5 + -1t) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {2, 5}