115=15t^2+120t+10

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Solution for 115=15t^2+120t+10 equation: 


Simplifying
115 = 15t2 + 120t + 10

Reorder the terms:
115 = 10 + 120t + 15t2

Solving
115 = 10 + 120t + 15t2

Solving for variable 't'.

Combine like terms: 115 + -10 = 105
105 + -120t + -15t2 = 10 + 120t + 15t2 + -10 + -120t + -15t2

Reorder the terms:
105 + -120t + -15t2 = 10 + -10 + 120t + -120t + 15t2 + -15t2

Combine like terms: 10 + -10 = 0
105 + -120t + -15t2 = 0 + 120t + -120t + 15t2 + -15t2
105 + -120t + -15t2 = 120t + -120t + 15t2 + -15t2

Combine like terms: 120t + -120t = 0
105 + -120t + -15t2 = 0 + 15t2 + -15t2
105 + -120t + -15t2 = 15t2 + -15t2

Combine like terms: 15t2 + -15t2 = 0
105 + -120t + -15t2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(7 + -8t + -1t2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(7 + -8t + -1t2)' equal to zero and attempt to solve:

Simplifying
7 + -8t + -1t2 = 0

Solving
7 + -8t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + 8t + t2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 8t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + 8t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 8t + t2 = 0 + 7
8t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
8t + t2 = 7

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 = 7 + 16

Reorder the terms:
16 + 8t + t2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + 8t + t2 = 23

Factor a perfect square on the left side:
(t + 4)(t + 4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(t + 4) equal to 4.795831523 and -4.795831523.


Subproblem 1
t + 4 = 4.795831523

Simplifying
t + 4 = 4.795831523

Reorder the terms:
4 + t = 4.795831523

Solving
4 + t = 4.795831523

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 = 4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + t = 4.795831523 + -4
t = 4.795831523 + -4

Combine like terms: 4.795831523 + -4 = 0.795831523
t = 0.795831523

Simplifying
t = 0.795831523


Subproblem 2
t + 4 = -4.795831523

Simplifying
t + 4 = -4.795831523

Reorder the terms:
4 + t = -4.795831523

Solving
4 + t = -4.795831523

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 = -4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + t = -4.795831523 + -4
t = -4.795831523 + -4

Combine like terms: -4.795831523 + -4 = -8.795831523
t = -8.795831523

Simplifying
t = -8.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.795831523, -8.795831523}
Solution
t = {0.795831523, -8.795831523}

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