-16(t^2-3t-22)=0

Solution for -16(t^2-3t-22)=0 equation:

Simplifying
-16(t2 + -3t + -22) = 0

Reorder the terms:
-16(-22 + -3t + t2) = 0
(-22 * -16 + -3t * -16 + t2 * -16) = 0
(352 + 48t + -16t2) = 0

Solving
352 + 48t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(22 + 3t + -1t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(22 + 3t + -1t2)' equal to zero and attempt to solve:

Simplifying
22 + 3t + -1t2 = 0

Solving
22 + 3t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-22 + -3t + t2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -3t + 22 + t2 = 0 + 22

Reorder the terms:
-22 + 22 + -3t + t2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -3t + t2 = 0 + 22
-3t + t2 = 0 + 22

Combine like terms: 0 + 22 = 22
-3t + t2 = 22

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 22 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + -3t + t2 = 24.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(t + -1.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
t + -1.5 = 4.924428901

Simplifying
t + -1.5 = 4.924428901

Reorder the terms:
-1.5 + t = 4.924428901

Solving
-1.5 + t = 4.924428901

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 4.924428901 + 1.5
t = 4.924428901 + 1.5

Combine like terms: 4.924428901 + 1.5 = 6.424428901
t = 6.424428901

Simplifying
t = 6.424428901

Subproblem 2
t + -1.5 = -4.924428901

Simplifying
t + -1.5 = -4.924428901

Reorder the terms:
-1.5 + t = -4.924428901

Solving
-1.5 + t = -4.924428901

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -4.924428901 + 1.5
t = -4.924428901 + 1.5

Combine like terms: -4.924428901 + 1.5 = -3.424428901
t = -3.424428901

Simplifying
t = -3.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.424428901, -3.424428901}
Solution
t = {6.424428901, -3.424428901}