16t^2+10t=6

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

Simplifying
16t2 + 10t = 6

Reorder the terms:
10t + 16t2 = 6

Solving
10t + 16t2 = 6

Solving for variable 't'.

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

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

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
t = {-1, 0.375}