(-16t*t)+24t+4=0

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Solution for (-16t*t)+24t+4=0 equation: 


Simplifying
(-16t * t) + 24t + 4 = 0

Multiply t * t
(-16t2) + 24t + 4 = 0

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

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

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 6t + (-4t2)) = 0

Ignore the factor 4.

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

Simplifying
1 + 6t + (-4t2) = 0

Solving
1 + 6t + (-4t2) = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -1.5t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.5t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.5t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.5t + t2 = 0 + 0.25
-1.5t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.5t + t2 = 0.25

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 0.25 + 0.5625

Combine like terms: 0.25 + 0.5625 = 0.8125
0.5625 + -1.5t + t2 = 0.8125

Factor a perfect square on the left side:
((t) + -0.75)((t) + -0.75) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
((t) + -0.75) equal to 0.901387819 and -0.901387819.


Subproblem 1
(t) + -0.75 = 0.901387819

Simplifying
(t) + -0.75 = 0.901387819
t + -0.75 = 0.901387819

Reorder the terms:
-0.75 + t = 0.901387819

Solving
-0.75 + t = 0.901387819

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 0.901387819 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 0.901387819 + 0.75
t = 0.901387819 + 0.75

Combine like terms: 0.901387819 + 0.75 = 1.651387819
t = 1.651387819

Simplifying
t = 1.651387819


Subproblem 2
(t) + -0.75 = -0.901387819

Simplifying
(t) + -0.75 = -0.901387819
t + -0.75 = -0.901387819

Reorder the terms:
-0.75 + t = -0.901387819

Solving
-0.75 + t = -0.901387819

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -0.901387819 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -0.901387819 + 0.75
t = -0.901387819 + 0.75

Combine like terms: -0.901387819 + 0.75 = -0.151387819
t = -0.151387819

Simplifying
t = -0.151387819


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.651387819, -0.151387819}
Solution
t = {1.651387819, -0.151387819}

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