30=48t-16t^2

Solution for 30=48t-16t^2 equation:

Simplifying
30 = 48t + -16t2

Solving
30 = 48t + -16t2

Solving for variable 't'.

Reorder the terms:
30 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
30 + -48t + 16t2 = 0 + -16t2 + 16t2
30 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
30 + -48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -24t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + -24t + 8t2)' equal to zero and attempt to solve:

Simplifying
15 + -24t + 8t2 = 0

Solving
15 + -24t + 8t2 = 0

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

Divide each side by '8'.
1.875 + -3t + t2 = 0

Move the constant term to the right:

Add '-1.875' to each side of the equation.
1.875 + -3t + -1.875 + t2 = 0 + -1.875

Reorder the terms:
1.875 + -1.875 + -3t + t2 = 0 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + -3t + t2 = 0 + -1.875
-3t + t2 = 0 + -1.875

Combine like terms: 0 + -1.875 = -1.875
-3t + t2 = -1.875

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 = -1.875 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -1.875 + 2.25

Combine like terms: -1.875 + 2.25 = 0.375
2.25 + -3t + t2 = 0.375

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(t + -1.5) equal to 0.612372436 and -0.612372436.

Subproblem 1
t + -1.5 = 0.612372436

Simplifying
t + -1.5 = 0.612372436

Reorder the terms:
-1.5 + t = 0.612372436

Solving
-1.5 + t = 0.612372436

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 = 0.612372436 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0.612372436 + 1.5
t = 0.612372436 + 1.5

Combine like terms: 0.612372436 + 1.5 = 2.112372436
t = 2.112372436

Simplifying
t = 2.112372436

Subproblem 2
t + -1.5 = -0.612372436

Simplifying
t + -1.5 = -0.612372436

Reorder the terms:
-1.5 + t = -0.612372436

Solving
-1.5 + t = -0.612372436

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 = -0.612372436 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -0.612372436 + 1.5
t = -0.612372436 + 1.5

Combine like terms: -0.612372436 + 1.5 = 0.887627564
t = 0.887627564

Simplifying
t = 0.887627564

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.112372436, 0.887627564}
Solution
t = {2.112372436, 0.887627564}