-t^2=100-20t

Solution for -t^2=100-20t equation:

Simplifying
-1t2 = 100 + -20t

Solving
-1t2 = 100 + -20t

Solving for variable 't'.

Reorder the terms:
-100 + 20t + -1t2 = 100 + -20t + -100 + 20t

Reorder the terms:
-100 + 20t + -1t2 = 100 + -100 + -20t + 20t

Combine like terms: 100 + -100 = 0
-100 + 20t + -1t2 = 0 + -20t + 20t
-100 + 20t + -1t2 = -20t + 20t

Combine like terms: -20t + 20t = 0
-100 + 20t + -1t2 = 0

Factor a trinomial.
(-10 + t)(10 + -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 '(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
Solution
t = {10, 10}