5t^2+10t-320=0

Solution for 5t^2+10t-320=0 equation:

Simplifying
5t2 + 10t + -320 = 0

Reorder the terms:
-320 + 10t + 5t2 = 0

Solving
-320 + 10t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-64 + 2t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-64 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
-64 + 2t + t2 = 0

Solving
-64 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 2t + 64 + t2 = 0 + 64

Reorder the terms:
-64 + 64 + 2t + t2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 2t + t2 = 0 + 64
2t + t2 = 0 + 64

Combine like terms: 0 + 64 = 64
2t + t2 = 64

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 = 64 + 1

Reorder the terms:
1 + 2t + t2 = 64 + 1

Combine like terms: 64 + 1 = 65
1 + 2t + t2 = 65

Factor a perfect square on the left side:
(t + 1)(t + 1) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(t + 1) equal to 8.062257748 and -8.062257748.

Subproblem 1
t + 1 = 8.062257748

Simplifying
t + 1 = 8.062257748

Reorder the terms:
1 + t = 8.062257748

Solving
1 + t = 8.062257748

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 = 8.062257748 + -1

Combine like terms: 1 + -1 = 0
0 + t = 8.062257748 + -1
t = 8.062257748 + -1

Combine like terms: 8.062257748 + -1 = 7.062257748
t = 7.062257748

Simplifying
t = 7.062257748

Subproblem 2
t + 1 = -8.062257748

Simplifying
t + 1 = -8.062257748

Reorder the terms:
1 + t = -8.062257748

Solving
1 + t = -8.062257748

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 = -8.062257748 + -1

Combine like terms: 1 + -1 = 0
0 + t = -8.062257748 + -1
t = -8.062257748 + -1

Combine like terms: -8.062257748 + -1 = -9.062257748
t = -9.062257748

Simplifying
t = -9.062257748

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.062257748, -9.062257748}
Solution
t = {7.062257748, -9.062257748}