8t-20+t^2=0

Solution for 8t-20+t^2=0 equation:

Simplifying
8t + -20 + t2 = 0

Reorder the terms:
-20 + 8t + t2 = 0

Solving
-20 + 8t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-10 + -1t)(2 + -1t) = 0

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

Simplifying
-10 + -1t = 0

Solving
-10 + -1t = 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 + -1t = 0 + 10

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

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

Divide each side by '-1'.
t = -10

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