-16t^2+40t+3=10

Solution for -16t^2+40t+3=10 equation:

Simplifying
-16t2 + 40t + 3 = 10

Reorder the terms:
3 + 40t + -16t2 = 10

Solving
3 + 40t + -16t2 = 10

Solving for variable 't'.

Reorder the terms:
3 + -10 + 40t + -16t2 = 10 + -10

Combine like terms: 3 + -10 = -7
-7 + 40t + -16t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-7 + 40t + -16t2 = 0

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

Divide each side by '-16'.
0.4375 + -2.5t + t2 = 0

Move the constant term to the right:

Add '-0.4375' to each side of the equation.
0.4375 + -2.5t + -0.4375 + t2 = 0 + -0.4375

Reorder the terms:
0.4375 + -0.4375 + -2.5t + t2 = 0 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + -2.5t + t2 = 0 + -0.4375
-2.5t + t2 = 0 + -0.4375

Combine like terms: 0 + -0.4375 = -0.4375
-2.5t + t2 = -0.4375

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = -0.4375 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = -0.4375 + 1.5625

Combine like terms: -0.4375 + 1.5625 = 1.125
1.5625 + -2.5t + t2 = 1.125

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 1.125

Calculate the square root of the right side: 1.060660172

Break this problem into two subproblems by setting 
(t + -1.25) equal to 1.060660172 and -1.060660172.

Subproblem 1
t + -1.25 = 1.060660172

Simplifying
t + -1.25 = 1.060660172

Reorder the terms:
-1.25 + t = 1.060660172

Solving
-1.25 + t = 1.060660172

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 1.060660172 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 1.060660172 + 1.25
t = 1.060660172 + 1.25

Combine like terms: 1.060660172 + 1.25 = 2.310660172
t = 2.310660172

Simplifying
t = 2.310660172

Subproblem 2
t + -1.25 = -1.060660172

Simplifying
t + -1.25 = -1.060660172

Reorder the terms:
-1.25 + t = -1.060660172

Solving
-1.25 + t = -1.060660172

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -1.060660172 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -1.060660172 + 1.25
t = -1.060660172 + 1.25

Combine like terms: -1.060660172 + 1.25 = 0.189339828
t = 0.189339828

Simplifying
t = 0.189339828

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.310660172, 0.189339828}