10=-16t^2+20t+6

Solution for 10=-16t^2+20t+6 equation:

Simplifying
10 = -16t2 + 20t + 6

Reorder the terms:
10 = 6 + 20t + -16t2

Solving
10 = 6 + 20t + -16t2

Solving for variable 't'.

Combine like terms: 10 + -6 = 4
4 + -20t + 16t2 = 6 + 20t + -16t2 + -6 + -20t + 16t2

Reorder the terms:
4 + -20t + 16t2 = 6 + -6 + 20t + -20t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
4 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2
4 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2

Combine like terms: 20t + -20t = 0
4 + -20t + 16t2 = 0 + -16t2 + 16t2
4 + -20t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
4 + -20t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -5t + 4t2) = 0

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Solution
t = {0.25, 1}