15t^2+120t+10=0

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Solution for 15t^2+120t+10=0 equation: 


Simplifying
15t2 + 120t + 10 = 0

Reorder the terms:
10 + 120t + 15t2 = 0

Solving
10 + 120t + 15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 24t + 3t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + 24t + 3t2)' equal to zero and attempt to solve:

Simplifying
2 + 24t + 3t2 = 0

Solving
2 + 24t + 3t2 = 0

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

Divide each side by '3'.
0.6666666667 + 8t + t2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 8t + -0.6666666667 + t2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 8t + t2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 8t + t2 = 0 + -0.6666666667
8t + t2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
8t + t2 = -0.6666666667

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = -0.6666666667 + 16

Reorder the terms:
16 + 8t + t2 = -0.6666666667 + 16

Combine like terms: -0.6666666667 + 16 = 15.3333333333
16 + 8t + t2 = 15.3333333333

Factor a perfect square on the left side:
(t + 4)(t + 4) = 15.3333333333

Calculate the square root of the right side: 3.915780041

Break this problem into two subproblems by setting 
(t + 4) equal to 3.915780041 and -3.915780041.


Subproblem 1
t + 4 = 3.915780041

Simplifying
t + 4 = 3.915780041

Reorder the terms:
4 + t = 3.915780041

Solving
4 + t = 3.915780041

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 3.915780041 + -4

Combine like terms: 4 + -4 = 0
0 + t = 3.915780041 + -4
t = 3.915780041 + -4

Combine like terms: 3.915780041 + -4 = -0.084219959
t = -0.084219959

Simplifying
t = -0.084219959


Subproblem 2
t + 4 = -3.915780041

Simplifying
t + 4 = -3.915780041

Reorder the terms:
4 + t = -3.915780041

Solving
4 + t = -3.915780041

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -3.915780041 + -4

Combine like terms: 4 + -4 = 0
0 + t = -3.915780041 + -4
t = -3.915780041 + -4

Combine like terms: -3.915780041 + -4 = -7.915780041
t = -7.915780041

Simplifying
t = -7.915780041


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.084219959, -7.915780041}
Solution
t = {-0.084219959, -7.915780041}

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