16t^2-150t-60=0

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Solution for 16t^2-150t-60=0 equation: 


Simplifying
16t2 + -150t + -60 = 0

Reorder the terms:
-60 + -150t + 16t2 = 0

Solving
-60 + -150t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -75t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + -75t + 8t2)' equal to zero and attempt to solve:

Simplifying
-30 + -75t + 8t2 = 0

Solving
-30 + -75t + 8t2 = 0

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

Divide each side by '8'.
-3.75 + -9.375t + t2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -9.375t + 3.75 + t2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -9.375t + t2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -9.375t + t2 = 0 + 3.75
-9.375t + t2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-9.375t + t2 = 3.75

The t term is -9.375t.  Take half its coefficient (-4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
-9.375t + 21.97265625 + t2 = 3.75 + 21.97265625

Reorder the terms:
21.97265625 + -9.375t + t2 = 3.75 + 21.97265625

Combine like terms: 3.75 + 21.97265625 = 25.72265625
21.97265625 + -9.375t + t2 = 25.72265625

Factor a perfect square on the left side:
(t + -4.6875)(t + -4.6875) = 25.72265625

Calculate the square root of the right side: 5.071750807

Break this problem into two subproblems by setting 
(t + -4.6875) equal to 5.071750807 and -5.071750807.


Subproblem 1
t + -4.6875 = 5.071750807

Simplifying
t + -4.6875 = 5.071750807

Reorder the terms:
-4.6875 + t = 5.071750807

Solving
-4.6875 + t = 5.071750807

Solving for variable 't'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + t = 5.071750807 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + t = 5.071750807 + 4.6875
t = 5.071750807 + 4.6875

Combine like terms: 5.071750807 + 4.6875 = 9.759250807
t = 9.759250807

Simplifying
t = 9.759250807


Subproblem 2
t + -4.6875 = -5.071750807

Simplifying
t + -4.6875 = -5.071750807

Reorder the terms:
-4.6875 + t = -5.071750807

Solving
-4.6875 + t = -5.071750807

Solving for variable 't'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + t = -5.071750807 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + t = -5.071750807 + 4.6875
t = -5.071750807 + 4.6875

Combine like terms: -5.071750807 + 4.6875 = -0.384250807
t = -0.384250807

Simplifying
t = -0.384250807


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.759250807, -0.384250807}
Solution
t = {9.759250807, -0.384250807}

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