-16t^2+120t+1500=0

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Solution for -16t^2+120t+1500=0 equation: 


Simplifying
-16t2 + 120t + 1500 = 0

Reorder the terms:
1500 + 120t + -16t2 = 0

Solving
1500 + 120t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(375 + 30t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(375 + 30t + -4t2)' equal to zero and attempt to solve:

Simplifying
375 + 30t + -4t2 = 0

Solving
375 + 30t + -4t2 = 0

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

Divide each side by '-4'.
-93.75 + -7.5t + t2 = 0

Move the constant term to the right:

Add '93.75' to each side of the equation.
-93.75 + -7.5t + 93.75 + t2 = 0 + 93.75

Reorder the terms:
-93.75 + 93.75 + -7.5t + t2 = 0 + 93.75

Combine like terms: -93.75 + 93.75 = 0.00
0.00 + -7.5t + t2 = 0 + 93.75
-7.5t + t2 = 0 + 93.75

Combine like terms: 0 + 93.75 = 93.75
-7.5t + t2 = 93.75

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = 93.75 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = 93.75 + 14.0625

Combine like terms: 93.75 + 14.0625 = 107.8125
14.0625 + -7.5t + t2 = 107.8125

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 107.8125

Calculate the square root of the right side: 10.383279829

Break this problem into two subproblems by setting 
(t + -3.75) equal to 10.383279829 and -10.383279829.


Subproblem 1
t + -3.75 = 10.383279829

Simplifying
t + -3.75 = 10.383279829

Reorder the terms:
-3.75 + t = 10.383279829

Solving
-3.75 + t = 10.383279829

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 10.383279829 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 10.383279829 + 3.75
t = 10.383279829 + 3.75

Combine like terms: 10.383279829 + 3.75 = 14.133279829
t = 14.133279829

Simplifying
t = 14.133279829


Subproblem 2
t + -3.75 = -10.383279829

Simplifying
t + -3.75 = -10.383279829

Reorder the terms:
-3.75 + t = -10.383279829

Solving
-3.75 + t = -10.383279829

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -10.383279829 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -10.383279829 + 3.75
t = -10.383279829 + 3.75

Combine like terms: -10.383279829 + 3.75 = -6.633279829
t = -6.633279829

Simplifying
t = -6.633279829


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.133279829, -6.633279829}
Solution
t = {14.133279829, -6.633279829}

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