-16t(t-6)=-204

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Solution for -16t(t-6)=-204 equation: 


Simplifying
-16t(t + -6) = -204

Reorder the terms:
-16t(-6 + t) = -204
(-6 * -16t + t * -16t) = -204
(96t + -16t2) = -204

Solving
96t + -16t2 = -204

Solving for variable 't'.

Reorder the terms:
204 + 96t + -16t2 = -204 + 204

Combine like terms: -204 + 204 = 0
204 + 96t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(51 + 24t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(51 + 24t + -4t2)' equal to zero and attempt to solve:

Simplifying
51 + 24t + -4t2 = 0

Solving
51 + 24t + -4t2 = 0

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

Divide each side by '-4'.
-12.75 + -6t + t2 = 0

Move the constant term to the right:

Add '12.75' to each side of the equation.
-12.75 + -6t + 12.75 + t2 = 0 + 12.75

Reorder the terms:
-12.75 + 12.75 + -6t + t2 = 0 + 12.75

Combine like terms: -12.75 + 12.75 = 0.00
0.00 + -6t + t2 = 0 + 12.75
-6t + t2 = 0 + 12.75

Combine like terms: 0 + 12.75 = 12.75
-6t + t2 = 12.75

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 12.75 + 9

Reorder the terms:
9 + -6t + t2 = 12.75 + 9

Combine like terms: 12.75 + 9 = 21.75
9 + -6t + t2 = 21.75

Factor a perfect square on the left side:
(t + -3)(t + -3) = 21.75

Calculate the square root of the right side: 4.663689527

Break this problem into two subproblems by setting 
(t + -3) equal to 4.663689527 and -4.663689527.


Subproblem 1
t + -3 = 4.663689527

Simplifying
t + -3 = 4.663689527

Reorder the terms:
-3 + t = 4.663689527

Solving
-3 + t = 4.663689527

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 4.663689527 + 3

Combine like terms: -3 + 3 = 0
0 + t = 4.663689527 + 3
t = 4.663689527 + 3

Combine like terms: 4.663689527 + 3 = 7.663689527
t = 7.663689527

Simplifying
t = 7.663689527


Subproblem 2
t + -3 = -4.663689527

Simplifying
t + -3 = -4.663689527

Reorder the terms:
-3 + t = -4.663689527

Solving
-3 + t = -4.663689527

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -4.663689527 + 3

Combine like terms: -3 + 3 = 0
0 + t = -4.663689527 + 3
t = -4.663689527 + 3

Combine like terms: -4.663689527 + 3 = -1.663689527
t = -1.663689527

Simplifying
t = -1.663689527


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.663689527, -1.663689527}
Solution
t = {7.663689527, -1.663689527}

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