5t^2+25t-20=0

Solution for 5t^2+25t-20=0 equation:

Simplifying
5t2 + 25t + -20 = 0

Reorder the terms:
-20 + 25t + 5t2 = 0

Solving
-20 + 25t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 5t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + 5t + t2)' equal to zero and attempt to solve:

Simplifying
-4 + 5t + t2 = 0

Solving
-4 + 5t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 5t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5t + t2 = 0 + 4
5t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
5t + t2 = 4

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = 4 + 6.25

Reorder the terms:
6.25 + 5t + t2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5t + t2 = 10.25

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(t + 2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
t + 2.5 = 3.201562119

Simplifying
t + 2.5 = 3.201562119

Reorder the terms:
2.5 + t = 3.201562119

Solving
2.5 + t = 3.201562119

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 3.201562119 + -2.5
t = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
t = 0.701562119

Simplifying
t = 0.701562119

Subproblem 2
t + 2.5 = -3.201562119

Simplifying
t + 2.5 = -3.201562119

Reorder the terms:
2.5 + t = -3.201562119

Solving
2.5 + t = -3.201562119

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -3.201562119 + -2.5
t = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
t = -5.701562119

Simplifying
t = -5.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.701562119, -5.701562119}
Solution
t = {0.701562119, -5.701562119}