-16t^2+96t+230=0

Solution for -16t^2+96t+230=0 equation:

Simplifying
-16t2 + 96t + 230 = 0

Reorder the terms:
230 + 96t + -16t2 = 0

Solving
230 + 96t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(115 + 48t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(115 + 48t + -8t2)' equal to zero and attempt to solve:

Simplifying
115 + 48t + -8t2 = 0

Solving
115 + 48t + -8t2 = 0

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

Divide each side by '-8'.
-14.375 + -6t + t2 = 0

Move the constant term to the right:

Add '14.375' to each side of the equation.
-14.375 + -6t + 14.375 + t2 = 0 + 14.375

Reorder the terms:
-14.375 + 14.375 + -6t + t2 = 0 + 14.375

Combine like terms: -14.375 + 14.375 = 0.000
0.000 + -6t + t2 = 0 + 14.375
-6t + t2 = 0 + 14.375

Combine like terms: 0 + 14.375 = 14.375
-6t + t2 = 14.375

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 14.375 + 9

Reorder the terms:
9 + -6t + t2 = 14.375 + 9

Combine like terms: 14.375 + 9 = 23.375
9 + -6t + t2 = 23.375

Factor a perfect square on the left side:
(t + -3)(t + -3) = 23.375

Calculate the square root of the right side: 4.834769901

Break this problem into two subproblems by setting 
(t + -3) equal to 4.834769901 and -4.834769901.

Subproblem 1
t + -3 = 4.834769901

Simplifying
t + -3 = 4.834769901

Reorder the terms:
-3 + t = 4.834769901

Solving
-3 + t = 4.834769901

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 4.834769901 + 3

Combine like terms: -3 + 3 = 0
0 + t = 4.834769901 + 3
t = 4.834769901 + 3

Combine like terms: 4.834769901 + 3 = 7.834769901
t = 7.834769901

Simplifying
t = 7.834769901

Subproblem 2
t + -3 = -4.834769901

Simplifying
t + -3 = -4.834769901

Reorder the terms:
-3 + t = -4.834769901

Solving
-3 + t = -4.834769901

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -4.834769901 + 3

Combine like terms: -3 + 3 = 0
0 + t = -4.834769901 + 3
t = -4.834769901 + 3

Combine like terms: -4.834769901 + 3 = -1.834769901
t = -1.834769901

Simplifying
t = -1.834769901

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.834769901, -1.834769901}
Solution
t = {7.834769901, -1.834769901}