-16t^2+48t+1500=0

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Solution for -16t^2+48t+1500=0 equation: 


Simplifying
-16t2 + 48t + 1500 = 0

Reorder the terms:
1500 + 48t + -16t2 = 0

Solving
1500 + 48t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(375 + 12t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(375 + 12t + -4t2)' equal to zero and attempt to solve:

Simplifying
375 + 12t + -4t2 = 0

Solving
375 + 12t + -4t2 = 0

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

Divide each side by '-4'.
-93.75 + -3t + t2 = 0

Move the constant term to the right:

Add '93.75' to each side of the equation.
-93.75 + -3t + 93.75 + t2 = 0 + 93.75

Reorder the terms:
-93.75 + 93.75 + -3t + t2 = 0 + 93.75

Combine like terms: -93.75 + 93.75 = 0.00
0.00 + -3t + t2 = 0 + 93.75
-3t + t2 = 0 + 93.75

Combine like terms: 0 + 93.75 = 93.75
-3t + t2 = 93.75

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 93.75 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 93.75 + 2.25

Combine like terms: 93.75 + 2.25 = 96
2.25 + -3t + t2 = 96

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(t + -1.5) equal to 9.797958971 and -9.797958971.


Subproblem 1
t + -1.5 = 9.797958971

Simplifying
t + -1.5 = 9.797958971

Reorder the terms:
-1.5 + t = 9.797958971

Solving
-1.5 + t = 9.797958971

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 9.797958971 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 9.797958971 + 1.5
t = 9.797958971 + 1.5

Combine like terms: 9.797958971 + 1.5 = 11.297958971
t = 11.297958971

Simplifying
t = 11.297958971


Subproblem 2
t + -1.5 = -9.797958971

Simplifying
t + -1.5 = -9.797958971

Reorder the terms:
-1.5 + t = -9.797958971

Solving
-1.5 + t = -9.797958971

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -9.797958971 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -9.797958971 + 1.5
t = -9.797958971 + 1.5

Combine like terms: -9.797958971 + 1.5 = -8.297958971
t = -8.297958971

Simplifying
t = -8.297958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.297958971, -8.297958971}
Solution
t = {11.297958971, -8.297958971}

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