-16t^2-30t+60=0

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Solution for -16t^2-30t+60=0 equation: 


Simplifying
-16t2 + -30t + 60 = 0

Reorder the terms:
60 + -30t + -16t2 = 0

Solving
60 + -30t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -15t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(30 + -15t + -8t2)' equal to zero and attempt to solve:

Simplifying
30 + -15t + -8t2 = 0

Solving
30 + -15t + -8t2 = 0

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

Divide each side by '-8'.
-3.75 + 1.875t + t2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 1.875t + 3.75 + t2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 1.875t + t2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 1.875t + t2 = 0 + 3.75
1.875t + t2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
1.875t + t2 = 3.75

The t term is 1.875t.  Take half its coefficient (0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
1.875t + 0.87890625 + t2 = 3.75 + 0.87890625

Reorder the terms:
0.87890625 + 1.875t + t2 = 3.75 + 0.87890625

Combine like terms: 3.75 + 0.87890625 = 4.62890625
0.87890625 + 1.875t + t2 = 4.62890625

Factor a perfect square on the left side:
(t + 0.9375)(t + 0.9375) = 4.62890625

Calculate the square root of the right side: 2.15148931

Break this problem into two subproblems by setting 
(t + 0.9375) equal to 2.15148931 and -2.15148931.


Subproblem 1
t + 0.9375 = 2.15148931

Simplifying
t + 0.9375 = 2.15148931

Reorder the terms:
0.9375 + t = 2.15148931

Solving
0.9375 + t = 2.15148931

Solving for variable 't'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + t = 2.15148931 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = 2.15148931 + -0.9375
t = 2.15148931 + -0.9375

Combine like terms: 2.15148931 + -0.9375 = 1.21398931
t = 1.21398931

Simplifying
t = 1.21398931


Subproblem 2
t + 0.9375 = -2.15148931

Simplifying
t + 0.9375 = -2.15148931

Reorder the terms:
0.9375 + t = -2.15148931

Solving
0.9375 + t = -2.15148931

Solving for variable 't'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + t = -2.15148931 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = -2.15148931 + -0.9375
t = -2.15148931 + -0.9375

Combine like terms: -2.15148931 + -0.9375 = -3.08898931
t = -3.08898931

Simplifying
t = -3.08898931


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.21398931, -3.08898931}
Solution
t = {1.21398931, -3.08898931}

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