-16t^2+72t-12=0

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Solution for -16t^2+72t-12=0 equation: 


Simplifying
-16t2 + 72t + -12 = 0

Reorder the terms:
-12 + 72t + -16t2 = 0

Solving
-12 + 72t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 18t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + 18t + -4t2)' equal to zero and attempt to solve:

Simplifying
-3 + 18t + -4t2 = 0

Solving
-3 + 18t + -4t2 = 0

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

Divide each side by '-4'.
0.75 + -4.5t + t2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -4.5t + -0.75 + t2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -4.5t + t2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -4.5t + t2 = 0 + -0.75
-4.5t + t2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-4.5t + t2 = -0.75

The t term is -4.5t.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5t + 5.0625 + t2 = -0.75 + 5.0625

Reorder the terms:
5.0625 + -4.5t + t2 = -0.75 + 5.0625

Combine like terms: -0.75 + 5.0625 = 4.3125
5.0625 + -4.5t + t2 = 4.3125

Factor a perfect square on the left side:
(t + -2.25)(t + -2.25) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(t + -2.25) equal to 2.076655966 and -2.076655966.


Subproblem 1
t + -2.25 = 2.076655966

Simplifying
t + -2.25 = 2.076655966

Reorder the terms:
-2.25 + t = 2.076655966

Solving
-2.25 + t = 2.076655966

Solving for variable 't'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + t = 2.076655966 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + t = 2.076655966 + 2.25
t = 2.076655966 + 2.25

Combine like terms: 2.076655966 + 2.25 = 4.326655966
t = 4.326655966

Simplifying
t = 4.326655966


Subproblem 2
t + -2.25 = -2.076655966

Simplifying
t + -2.25 = -2.076655966

Reorder the terms:
-2.25 + t = -2.076655966

Solving
-2.25 + t = -2.076655966

Solving for variable 't'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + t = -2.076655966 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + t = -2.076655966 + 2.25
t = -2.076655966 + 2.25

Combine like terms: -2.076655966 + 2.25 = 0.173344034
t = 0.173344034

Simplifying
t = 0.173344034


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.326655966, 0.173344034}
Solution
t = {4.326655966, 0.173344034}

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