9t^2+39t-144=0

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Solution for 9t^2+39t-144=0 equation: 


Simplifying
9t2 + 39t + -144 = 0

Reorder the terms:
-144 + 39t + 9t2 = 0

Solving
-144 + 39t + 9t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-48 + 13t + 3t2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-48 + 13t + 3t2)' equal to zero and attempt to solve:

Simplifying
-48 + 13t + 3t2 = 0

Solving
-48 + 13t + 3t2 = 0

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

Divide each side by '3'.
-16 + 4.333333333t + t2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4.333333333t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + 4.333333333t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4.333333333t + t2 = 0 + 16
4.333333333t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
4.333333333t + t2 = 16

The t term is 4.333333333t.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333t + 4.694444446 + t2 = 16 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333t + t2 = 16 + 4.694444446

Combine like terms: 16 + 4.694444446 = 20.694444446
4.694444446 + 4.333333333t + t2 = 20.694444446

Factor a perfect square on the left side:
(t + 2.166666667)(t + 2.166666667) = 20.694444446

Calculate the square root of the right side: 4.549114688

Break this problem into two subproblems by setting 
(t + 2.166666667) equal to 4.549114688 and -4.549114688.


Subproblem 1
t + 2.166666667 = 4.549114688

Simplifying
t + 2.166666667 = 4.549114688

Reorder the terms:
2.166666667 + t = 4.549114688

Solving
2.166666667 + t = 4.549114688

Solving for variable 't'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + t = 4.549114688 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + t = 4.549114688 + -2.166666667
t = 4.549114688 + -2.166666667

Combine like terms: 4.549114688 + -2.166666667 = 2.382448021
t = 2.382448021

Simplifying
t = 2.382448021


Subproblem 2
t + 2.166666667 = -4.549114688

Simplifying
t + 2.166666667 = -4.549114688

Reorder the terms:
2.166666667 + t = -4.549114688

Solving
2.166666667 + t = -4.549114688

Solving for variable 't'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + t = -4.549114688 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + t = -4.549114688 + -2.166666667
t = -4.549114688 + -2.166666667

Combine like terms: -4.549114688 + -2.166666667 = -6.715781355
t = -6.715781355

Simplifying
t = -6.715781355


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.382448021, -6.715781355}
Solution
t = {2.382448021, -6.715781355}

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