100=20t+3t^2

Solution for 100=20t+3t^2 equation:

Simplifying
100 = 20t + 3t2

Solving
100 = 20t + 3t2

Solving for variable 't'.

Reorder the terms:
100 + -20t + -3t2 = 20t + -20t + 3t2 + -3t2

Combine like terms: 20t + -20t = 0
100 + -20t + -3t2 = 0 + 3t2 + -3t2
100 + -20t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
100 + -20t + -3t2 = 0

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

Subproblem 1
Set the factor '(10 + -3t)' equal to zero and attempt to solve:

Simplifying
10 + -3t = 0

Solving
10 + -3t = 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 + -3t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3t = 0 + -10
-3t = 0 + -10

Combine like terms: 0 + -10 = -10
-3t = -10

Divide each side by '-3'.
t = 3.333333333

Simplifying
t = 3.333333333
Subproblem 2
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
Solution
t = {3.333333333, -10}