-16t^2+24t+30=0

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Solution for -16t^2+24t+30=0 equation: 


Simplifying
-16t2 + 24t + 30 = 0

Reorder the terms:
30 + 24t + -16t2 = 0

Solving
30 + 24t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 12t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 12t + -8t2)' equal to zero and attempt to solve:

Simplifying
15 + 12t + -8t2 = 0

Solving
15 + 12t + -8t2 = 0

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

Divide each side by '-8'.
-1.875 + -1.5t + t2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -1.5t + 1.875 + t2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -1.5t + t2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -1.5t + t2 = 0 + 1.875
-1.5t + t2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-1.5t + t2 = 1.875

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 1.875 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 1.875 + 0.5625

Combine like terms: 1.875 + 0.5625 = 2.4375
0.5625 + -1.5t + t2 = 2.4375

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 2.4375

Calculate the square root of the right side: 1.5612495

Break this problem into two subproblems by setting 
(t + -0.75) equal to 1.5612495 and -1.5612495.


Subproblem 1
t + -0.75 = 1.5612495

Simplifying
t + -0.75 = 1.5612495

Reorder the terms:
-0.75 + t = 1.5612495

Solving
-0.75 + t = 1.5612495

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 1.5612495 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 1.5612495 + 0.75
t = 1.5612495 + 0.75

Combine like terms: 1.5612495 + 0.75 = 2.3112495
t = 2.3112495

Simplifying
t = 2.3112495


Subproblem 2
t + -0.75 = -1.5612495

Simplifying
t + -0.75 = -1.5612495

Reorder the terms:
-0.75 + t = -1.5612495

Solving
-0.75 + t = -1.5612495

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -1.5612495 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -1.5612495 + 0.75
t = -1.5612495 + 0.75

Combine like terms: -1.5612495 + 0.75 = -0.8112495
t = -0.8112495

Simplifying
t = -0.8112495


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.3112495, -0.8112495}
Solution
t = {2.3112495, -0.8112495}

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