0=-2(8t^2-4t-35)

Solution for 0=-2(8t^2-4t-35) equation:

Simplifying
0 = -2(8t2 + -4t + -35)

Reorder the terms:
0 = -2(-35 + -4t + 8t2)
0 = (-35 * -2 + -4t * -2 + 8t2 * -2)
0 = (70 + 8t + -16t2)

Solving
0 = 70 + 8t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -70 = -70
-70 + -8t + 16t2 = 70 + 8t + -16t2 + -70 + -8t + 16t2

Reorder the terms:
-70 + -8t + 16t2 = 70 + -70 + 8t + -8t + -16t2 + 16t2

Combine like terms: 70 + -70 = 0
-70 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2
-70 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2

Combine like terms: 8t + -8t = 0
-70 + -8t + 16t2 = 0 + -16t2 + 16t2
-70 + -8t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-70 + -8t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -4t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + -4t + 8t2)' equal to zero and attempt to solve:

Simplifying
-35 + -4t + 8t2 = 0

Solving
-35 + -4t + 8t2 = 0

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

Divide each side by '8'.
-4.375 + -0.5t + t2 = 0

Move the constant term to the right:

Add '4.375' to each side of the equation.
-4.375 + -0.5t + 4.375 + t2 = 0 + 4.375

Reorder the terms:
-4.375 + 4.375 + -0.5t + t2 = 0 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + -0.5t + t2 = 0 + 4.375
-0.5t + t2 = 0 + 4.375

Combine like terms: 0 + 4.375 = 4.375
-0.5t + t2 = 4.375

The t term is -0.5t.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5t + 0.0625 + t2 = 4.375 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = 4.375 + 0.0625

Combine like terms: 4.375 + 0.0625 = 4.4375
0.0625 + -0.5t + t2 = 4.4375

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = 4.4375

Calculate the square root of the right side: 2.106537443

Break this problem into two subproblems by setting 
(t + -0.25) equal to 2.106537443 and -2.106537443.

Subproblem 1
t + -0.25 = 2.106537443

Simplifying
t + -0.25 = 2.106537443

Reorder the terms:
-0.25 + t = 2.106537443

Solving
-0.25 + t = 2.106537443

Solving for variable 't'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + t = 2.106537443 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = 2.106537443 + 0.25
t = 2.106537443 + 0.25

Combine like terms: 2.106537443 + 0.25 = 2.356537443
t = 2.356537443

Simplifying
t = 2.356537443

Subproblem 2
t + -0.25 = -2.106537443

Simplifying
t + -0.25 = -2.106537443

Reorder the terms:
-0.25 + t = -2.106537443

Solving
-0.25 + t = -2.106537443

Solving for variable 't'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + t = -2.106537443 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = -2.106537443 + 0.25
t = -2.106537443 + 0.25

Combine like terms: -2.106537443 + 0.25 = -1.856537443
t = -1.856537443

Simplifying
t = -1.856537443

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.356537443, -1.856537443}
Solution
t = {2.356537443, -1.856537443}