2400=16t^2+400t

Solution for 2400=16t^2+400t equation:

Simplifying
2400 = 16t2 + 400t

Reorder the terms:
2400 = 400t + 16t2

Solving
2400 = 400t + 16t2

Solving for variable 't'.

Reorder the terms:
2400 + -400t + -16t2 = 400t + -400t + 16t2 + -16t2

Combine like terms: 400t + -400t = 0
2400 + -400t + -16t2 = 0 + 16t2 + -16t2
2400 + -400t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
2400 + -400t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(150 + -25t + -1t2) = 0

Factor a trinomial.
16((5 + -1t)(30 + t)) = 0

Ignore the factor 16.
Subproblem 1
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
Subproblem 2
Set the factor '(30 + t)' equal to zero and attempt to solve:

Simplifying
30 + t = 0

Solving
30 + t = 0

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

Add '-30' to each side of the equation.
30 + -30 + t = 0 + -30

Combine like terms: 30 + -30 = 0
0 + t = 0 + -30
t = 0 + -30

Combine like terms: 0 + -30 = -30
t = -30

Simplifying
t = -30
Solution
t = {5, -30}