-16t^2+46t+4=0

Solution for -16t^2+46t+4=0 equation:

Simplifying
-16t2 + 46t + 4 = 0

Reorder the terms:
4 + 46t + -16t2 = 0

Solving
4 + 46t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 23t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 23t + -8t2)' equal to zero and attempt to solve:

Simplifying
2 + 23t + -8t2 = 0

Solving
2 + 23t + -8t2 = 0

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

Divide each side by '-8'.
-0.25 + -2.875t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2.875t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2.875t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2.875t + t2 = 0 + 0.25
-2.875t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2.875t + t2 = 0.25

The t term is -2.875t.  Take half its coefficient (-1.4375).
Square it (2.06640625) and add it to both sides.

Add '2.06640625' to each side of the equation.
-2.875t + 2.06640625 + t2 = 0.25 + 2.06640625

Reorder the terms:
2.06640625 + -2.875t + t2 = 0.25 + 2.06640625

Combine like terms: 0.25 + 2.06640625 = 2.31640625
2.06640625 + -2.875t + t2 = 2.31640625

Factor a perfect square on the left side:
(t + -1.4375)(t + -1.4375) = 2.31640625

Calculate the square root of the right side: 1.521974458

Break this problem into two subproblems by setting 
(t + -1.4375) equal to 1.521974458 and -1.521974458.

Subproblem 1
t + -1.4375 = 1.521974458

Simplifying
t + -1.4375 = 1.521974458

Reorder the terms:
-1.4375 + t = 1.521974458

Solving
-1.4375 + t = 1.521974458

Solving for variable 't'.

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

Add '1.4375' to each side of the equation.
-1.4375 + 1.4375 + t = 1.521974458 + 1.4375

Combine like terms: -1.4375 + 1.4375 = 0.0000
0.0000 + t = 1.521974458 + 1.4375
t = 1.521974458 + 1.4375

Combine like terms: 1.521974458 + 1.4375 = 2.959474458
t = 2.959474458

Simplifying
t = 2.959474458

Subproblem 2
t + -1.4375 = -1.521974458

Simplifying
t + -1.4375 = -1.521974458

Reorder the terms:
-1.4375 + t = -1.521974458

Solving
-1.4375 + t = -1.521974458

Solving for variable 't'.

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

Add '1.4375' to each side of the equation.
-1.4375 + 1.4375 + t = -1.521974458 + 1.4375

Combine like terms: -1.4375 + 1.4375 = 0.0000
0.0000 + t = -1.521974458 + 1.4375
t = -1.521974458 + 1.4375

Combine like terms: -1.521974458 + 1.4375 = -0.084474458
t = -0.084474458

Simplifying
t = -0.084474458

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.959474458, -0.084474458}
Solution
t = {2.959474458, -0.084474458}