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

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

Simplifying
10(t) = -16t2 + 20t + 6

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

Solving
10t = 6 + 20t + -16t2

Solving for variable 't'.

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

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

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

Combine like terms: 6 + -6 = 0
-6 + -10t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2
-6 + -10t + 16t2 = 20t + -20t + -16t2 + 16t2

Combine like terms: 20t + -20t = 0
-6 + -10t + 16t2 = 0 + -16t2 + 16t2
-6 + -10t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + -10t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5t + 8t2) = 0

Factor a trinomial.
2((-3 + -8t)(1 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -8t)' equal to zero and attempt to solve:

Simplifying
-3 + -8t = 0

Solving
-3 + -8t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -8t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8t = 0 + 3
-8t = 0 + 3

Combine like terms: 0 + 3 = 3
-8t = 3

Divide each side by '-8'.
t = -0.375

Simplifying
t = -0.375
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 = {-0.375, 1}