10=-16t^2+23t+6

Solution for 10=-16t^2+23t+6 equation:

Simplifying
10 = -16t2 + 23t + 6

Reorder the terms:
10 = 6 + 23t + -16t2

Solving
10 = 6 + 23t + -16t2

Solving for variable 't'.

Combine like terms: 10 + -6 = 4
4 + -23t + 16t2 = 6 + 23t + -16t2 + -6 + -23t + 16t2

Reorder the terms:
4 + -23t + 16t2 = 6 + -6 + 23t + -23t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
4 + -23t + 16t2 = 0 + 23t + -23t + -16t2 + 16t2
4 + -23t + 16t2 = 23t + -23t + -16t2 + 16t2

Combine like terms: 23t + -23t = 0
4 + -23t + 16t2 = 0 + -16t2 + 16t2
4 + -23t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
4 + -23t + 16t2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
0.25 + -1.4375t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.4375t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.4375t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.4375t + t2 = 0 + -0.25
-1.4375t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.4375t + t2 = -0.25

The t term is -1.4375t.  Take half its coefficient (-0.71875).
Square it (0.5166015625) and add it to both sides.

Add '0.5166015625' to each side of the equation.
-1.4375t + 0.5166015625 + t2 = -0.25 + 0.5166015625

Reorder the terms:
0.5166015625 + -1.4375t + t2 = -0.25 + 0.5166015625

Combine like terms: -0.25 + 0.5166015625 = 0.2666015625
0.5166015625 + -1.4375t + t2 = 0.2666015625

Factor a perfect square on the left side:
(t + -0.71875)(t + -0.71875) = 0.2666015625

Calculate the square root of the right side: 0.516334739

Break this problem into two subproblems by setting 
(t + -0.71875) equal to 0.516334739 and -0.516334739.

Subproblem 1
t + -0.71875 = 0.516334739

Simplifying
t + -0.71875 = 0.516334739

Reorder the terms:
-0.71875 + t = 0.516334739

Solving
-0.71875 + t = 0.516334739

Solving for variable 't'.

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

Add '0.71875' to each side of the equation.
-0.71875 + 0.71875 + t = 0.516334739 + 0.71875

Combine like terms: -0.71875 + 0.71875 = 0.00000
0.00000 + t = 0.516334739 + 0.71875
t = 0.516334739 + 0.71875

Combine like terms: 0.516334739 + 0.71875 = 1.235084739
t = 1.235084739

Simplifying
t = 1.235084739

Subproblem 2
t + -0.71875 = -0.516334739

Simplifying
t + -0.71875 = -0.516334739

Reorder the terms:
-0.71875 + t = -0.516334739

Solving
-0.71875 + t = -0.516334739

Solving for variable 't'.

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

Add '0.71875' to each side of the equation.
-0.71875 + 0.71875 + t = -0.516334739 + 0.71875

Combine like terms: -0.71875 + 0.71875 = 0.00000
0.00000 + t = -0.516334739 + 0.71875
t = -0.516334739 + 0.71875

Combine like terms: -0.516334739 + 0.71875 = 0.202415261
t = 0.202415261

Simplifying
t = 0.202415261

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.235084739, 0.202415261}