4t^2-20t-60=0

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Solution for 4t^2-20t-60=0 equation: 


Simplifying
4t2 + -20t + -60 = 0

Reorder the terms:
-60 + -20t + 4t2 = 0

Solving
-60 + -20t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -5t + t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + -5t + t2)' equal to zero and attempt to solve:

Simplifying
-15 + -5t + t2 = 0

Solving
-15 + -5t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -5t + 15 + t2 = 0 + 15

Reorder the terms:
-15 + 15 + -5t + t2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -5t + t2 = 0 + 15
-5t + t2 = 0 + 15

Combine like terms: 0 + 15 = 15
-5t + t2 = 15

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 = 15 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 15 + 6.25

Combine like terms: 15 + 6.25 = 21.25
6.25 + -5t + t2 = 21.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(t + -2.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
t + -2.5 = 4.609772229

Simplifying
t + -2.5 = 4.609772229

Reorder the terms:
-2.5 + t = 4.609772229

Solving
-2.5 + t = 4.609772229

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 = 4.609772229 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 4.609772229 + 2.5
t = 4.609772229 + 2.5

Combine like terms: 4.609772229 + 2.5 = 7.109772229
t = 7.109772229

Simplifying
t = 7.109772229


Subproblem 2
t + -2.5 = -4.609772229

Simplifying
t + -2.5 = -4.609772229

Reorder the terms:
-2.5 + t = -4.609772229

Solving
-2.5 + t = -4.609772229

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 = -4.609772229 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -4.609772229 + 2.5
t = -4.609772229 + 2.5

Combine like terms: -4.609772229 + 2.5 = -2.109772229
t = -2.109772229

Simplifying
t = -2.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.109772229, -2.109772229}
Solution
t = {7.109772229, -2.109772229}

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