6=-16t^2+24t+1

Solution for 6=-16t^2+24t+1 equation:

Simplifying
6 = -16t2 + 24t + 1

Reorder the terms:
6 = 1 + 24t + -16t2

Solving
6 = 1 + 24t + -16t2

Solving for variable 't'.

Combine like terms: 6 + -1 = 5
5 + -24t + 16t2 = 1 + 24t + -16t2 + -1 + -24t + 16t2

Reorder the terms:
5 + -24t + 16t2 = 1 + -1 + 24t + -24t + -16t2 + 16t2

Combine like terms: 1 + -1 = 0
5 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2
5 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2

Combine like terms: 24t + -24t = 0
5 + -24t + 16t2 = 0 + -16t2 + 16t2
5 + -24t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
5 + -24t + 16t2 = 0

Factor a trinomial.
(1 + -4t)(5 + -4t) = 0

Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve:

Simplifying
1 + -4t = 0

Solving
1 + -4t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
Subproblem 2
Set the factor '(5 + -4t)' equal to zero and attempt to solve:

Simplifying
5 + -4t = 0

Solving
5 + -4t = 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 + -4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4t = 0 + -5
-4t = 0 + -5

Combine like terms: 0 + -5 = -5
-4t = -5

Divide each side by '-4'.
t = 1.25

Simplifying
t = 1.25
Solution
t = {0.25, 1.25}