0=5t^2+10t-80

Solution for 0=5t^2+10t-80 equation:

Simplifying
0 = 5t2 + 10t + -80

Reorder the terms:
0 = -80 + 10t + 5t2

Solving
0 = -80 + 10t + 5t2

Solving for variable 't'.

Combine like terms: 0 + 80 = 80
80 + -10t + -5t2 = -80 + 10t + 5t2 + 80 + -10t + -5t2

Reorder the terms:
80 + -10t + -5t2 = -80 + 80 + 10t + -10t + 5t2 + -5t2

Combine like terms: -80 + 80 = 0
80 + -10t + -5t2 = 0 + 10t + -10t + 5t2 + -5t2
80 + -10t + -5t2 = 10t + -10t + 5t2 + -5t2

Combine like terms: 10t + -10t = 0
80 + -10t + -5t2 = 0 + 5t2 + -5t2
80 + -10t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
80 + -10t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(16 + -2t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(16 + -2t + -1t2)' equal to zero and attempt to solve:

Simplifying
16 + -2t + -1t2 = 0

Solving
16 + -2t + -1t2 = 0

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

Divide each side by '-1'.
-16 + 2t + t2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 2t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + 2t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 2t + t2 = 0 + 16
2t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
2t + t2 = 16

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 16 + 1

Reorder the terms:
1 + 2t + t2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + 2t + t2 = 17

Factor a perfect square on the left side:
(t + 1)(t + 1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(t + 1) equal to 4.123105626 and -4.123105626.

Subproblem 1
t + 1 = 4.123105626

Simplifying
t + 1 = 4.123105626

Reorder the terms:
1 + t = 4.123105626

Solving
1 + t = 4.123105626

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + t = 4.123105626 + -1
t = 4.123105626 + -1

Combine like terms: 4.123105626 + -1 = 3.123105626
t = 3.123105626

Simplifying
t = 3.123105626

Subproblem 2
t + 1 = -4.123105626

Simplifying
t + 1 = -4.123105626

Reorder the terms:
1 + t = -4.123105626

Solving
1 + t = -4.123105626

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + t = -4.123105626 + -1
t = -4.123105626 + -1

Combine like terms: -4.123105626 + -1 = -5.123105626
t = -5.123105626

Simplifying
t = -5.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.123105626, -5.123105626}
Solution
t = {3.123105626, -5.123105626}