13t-t^2=30

Solution for 13t-t^2=30 equation:

Simplifying
13t + -1t2 = 30

Solving
13t + -1t2 = 30

Solving for variable 't'.

Reorder the terms:
-30 + 13t + -1t2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 13t + -1t2 = 0

Factor a trinomial.
(-10 + t)(3 + -1t) = 0

Subproblem 1
Set the factor '(-10 + t)' equal to zero and attempt to solve:

Simplifying
-10 + t = 0

Solving
-10 + t = 0

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

Add '10' to each side of the equation.
-10 + 10 + t = 0 + 10

Combine like terms: -10 + 10 = 0
0 + t = 0 + 10
t = 0 + 10

Combine like terms: 0 + 10 = 10
t = 10

Simplifying
t = 10
Subproblem 2
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
Solution
t = {10, 3}