-160=t^2+73t+6

Solution for -160=t^2+73t+6 equation:

Simplifying
-160 = t2 + 73t + 6

Reorder the terms:
-160 = 6 + 73t + t2

Solving
-160 = 6 + 73t + t2

Solving for variable 't'.

Combine like terms: -160 + -6 = -166
-166 + -73t + -1t2 = 6 + 73t + t2 + -6 + -73t + -1t2

Reorder the terms:
-166 + -73t + -1t2 = 6 + -6 + 73t + -73t + t2 + -1t2

Combine like terms: 6 + -6 = 0
-166 + -73t + -1t2 = 0 + 73t + -73t + t2 + -1t2
-166 + -73t + -1t2 = 73t + -73t + t2 + -1t2

Combine like terms: 73t + -73t = 0
-166 + -73t + -1t2 = 0 + t2 + -1t2
-166 + -73t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-166 + -73t + -1t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(166 + 73t + t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(166 + 73t + t2)' equal to zero and attempt to solve:

Simplifying
166 + 73t + t2 = 0

Solving
166 + 73t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-166' to each side of the equation.
166 + 73t + -166 + t2 = 0 + -166

Reorder the terms:
166 + -166 + 73t + t2 = 0 + -166

Combine like terms: 166 + -166 = 0
0 + 73t + t2 = 0 + -166
73t + t2 = 0 + -166

Combine like terms: 0 + -166 = -166
73t + t2 = -166

The t term is 73t.  Take half its coefficient (36.5).
Square it (1332.25) and add it to both sides.

Add '1332.25' to each side of the equation.
73t + 1332.25 + t2 = -166 + 1332.25

Reorder the terms:
1332.25 + 73t + t2 = -166 + 1332.25

Combine like terms: -166 + 1332.25 = 1166.25
1332.25 + 73t + t2 = 1166.25

Factor a perfect square on the left side:
(t + 36.5)(t + 36.5) = 1166.25

Calculate the square root of the right side: 34.150402633

Break this problem into two subproblems by setting 
(t + 36.5) equal to 34.150402633 and -34.150402633.

Subproblem 1
t + 36.5 = 34.150402633

Simplifying
t + 36.5 = 34.150402633

Reorder the terms:
36.5 + t = 34.150402633

Solving
36.5 + t = 34.150402633

Solving for variable 't'.

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

Add '-36.5' to each side of the equation.
36.5 + -36.5 + t = 34.150402633 + -36.5

Combine like terms: 36.5 + -36.5 = 0.0
0.0 + t = 34.150402633 + -36.5
t = 34.150402633 + -36.5

Combine like terms: 34.150402633 + -36.5 = -2.349597367
t = -2.349597367

Simplifying
t = -2.349597367

Subproblem 2
t + 36.5 = -34.150402633

Simplifying
t + 36.5 = -34.150402633

Reorder the terms:
36.5 + t = -34.150402633

Solving
36.5 + t = -34.150402633

Solving for variable 't'.

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

Add '-36.5' to each side of the equation.
36.5 + -36.5 + t = -34.150402633 + -36.5

Combine like terms: 36.5 + -36.5 = 0.0
0.0 + t = -34.150402633 + -36.5
t = -34.150402633 + -36.5

Combine like terms: -34.150402633 + -36.5 = -70.650402633
t = -70.650402633

Simplifying
t = -70.650402633

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-2.349597367, -70.650402633}
Solution
t = {-2.349597367, -70.650402633}