4t^2-16t-24=0

Solution for 4t^2-16t-24=0 equation:

Simplifying
4t2 + -16t + -24 = 0

Reorder the terms:
-24 + -16t + 4t2 = 0

Solving
-24 + -16t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -4t + t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -4t + t2)' equal to zero and attempt to solve:

Simplifying
-6 + -4t + t2 = 0

Solving
-6 + -4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -4t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -4t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -4t + t2 = 0 + 6
-4t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4t + t2 = 6

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 6 + 4

Reorder the terms:
4 + -4t + t2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + -4t + t2 = 10

Factor a perfect square on the left side:
(t + -2)(t + -2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(t + -2) equal to 3.16227766 and -3.16227766.

Subproblem 1
t + -2 = 3.16227766

Simplifying
t + -2 = 3.16227766

Reorder the terms:
-2 + t = 3.16227766

Solving
-2 + t = 3.16227766

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + t = 3.16227766 + 2
t = 3.16227766 + 2

Combine like terms: 3.16227766 + 2 = 5.16227766
t = 5.16227766

Simplifying
t = 5.16227766

Subproblem 2
t + -2 = -3.16227766

Simplifying
t + -2 = -3.16227766

Reorder the terms:
-2 + t = -3.16227766

Solving
-2 + t = -3.16227766

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + t = -3.16227766 + 2
t = -3.16227766 + 2

Combine like terms: -3.16227766 + 2 = -1.16227766
t = -1.16227766

Simplifying
t = -1.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.16227766, -1.16227766}
Solution
t = {5.16227766, -1.16227766}