130(t)=-16t^2+112t+6

Solution for 130(t)=-16t^2+112t+6 equation:

Simplifying
130(t) = -16t2 + 112t + 6

Reorder the terms:
130t = 6 + 112t + -16t2

Solving
130t = 6 + 112t + -16t2

Solving for variable 't'.

Reorder the terms:
-6 + 130t + -112t + 16t2 = 6 + 112t + -16t2 + -6 + -112t + 16t2

Combine like terms: 130t + -112t = 18t
-6 + 18t + 16t2 = 6 + 112t + -16t2 + -6 + -112t + 16t2

Reorder the terms:
-6 + 18t + 16t2 = 6 + -6 + 112t + -112t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
-6 + 18t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2
-6 + 18t + 16t2 = 112t + -112t + -16t2 + 16t2

Combine like terms: 112t + -112t = 0
-6 + 18t + 16t2 = 0 + -16t2 + 16t2
-6 + 18t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + 18t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 9t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 9t + 8t2)' equal to zero and attempt to solve:

Simplifying
-3 + 9t + 8t2 = 0

Solving
-3 + 9t + 8t2 = 0

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

Divide each side by '8'.
-0.375 + 1.125t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 1.125t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 1.125t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 1.125t + t2 = 0 + 0.375
1.125t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
1.125t + t2 = 0.375

The t term is 1.125t.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125t + 0.31640625 + t2 = 0.375 + 0.31640625

Reorder the terms:
0.31640625 + 1.125t + t2 = 0.375 + 0.31640625

Combine like terms: 0.375 + 0.31640625 = 0.69140625
0.31640625 + 1.125t + t2 = 0.69140625

Factor a perfect square on the left side:
(t + 0.5625)(t + 0.5625) = 0.69140625

Calculate the square root of the right side: 0.831508418

Break this problem into two subproblems by setting 
(t + 0.5625) equal to 0.831508418 and -0.831508418.

Subproblem 1
t + 0.5625 = 0.831508418

Simplifying
t + 0.5625 = 0.831508418

Reorder the terms:
0.5625 + t = 0.831508418

Solving
0.5625 + t = 0.831508418

Solving for variable 't'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + t = 0.831508418 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + t = 0.831508418 + -0.5625
t = 0.831508418 + -0.5625

Combine like terms: 0.831508418 + -0.5625 = 0.269008418
t = 0.269008418

Simplifying
t = 0.269008418

Subproblem 2
t + 0.5625 = -0.831508418

Simplifying
t + 0.5625 = -0.831508418

Reorder the terms:
0.5625 + t = -0.831508418

Solving
0.5625 + t = -0.831508418

Solving for variable 't'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + t = -0.831508418 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + t = -0.831508418 + -0.5625
t = -0.831508418 + -0.5625

Combine like terms: -0.831508418 + -0.5625 = -1.394008418
t = -1.394008418

Simplifying
t = -1.394008418

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.269008418, -1.394008418}
Solution
t = {0.269008418, -1.394008418}