-16t^2+48t+18=0

Solution for -16t^2+48t+18=0 equation:

Simplifying
-16t2 + 48t + 18 = 0

Reorder the terms:
18 + 48t + -16t2 = 0

Solving
18 + 48t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 24t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + 24t + -8t2)' equal to zero and attempt to solve:

Simplifying
9 + 24t + -8t2 = 0

Solving
9 + 24t + -8t2 = 0

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

Divide each side by '-8'.
-1.125 + -3t + t2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -3t + 1.125 + t2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -3t + t2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -3t + t2 = 0 + 1.125
-3t + t2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-3t + t2 = 1.125

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 = 1.125 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 1.125 + 2.25

Combine like terms: 1.125 + 2.25 = 3.375
2.25 + -3t + t2 = 3.375

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 3.375

Calculate the square root of the right side: 1.837117307

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.837117307 and -1.837117307.

Subproblem 1
t + -1.5 = 1.837117307

Simplifying
t + -1.5 = 1.837117307

Reorder the terms:
-1.5 + t = 1.837117307

Solving
-1.5 + t = 1.837117307

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 = 1.837117307 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.837117307 + 1.5
t = 1.837117307 + 1.5

Combine like terms: 1.837117307 + 1.5 = 3.337117307
t = 3.337117307

Simplifying
t = 3.337117307

Subproblem 2
t + -1.5 = -1.837117307

Simplifying
t + -1.5 = -1.837117307

Reorder the terms:
-1.5 + t = -1.837117307

Solving
-1.5 + t = -1.837117307

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 = -1.837117307 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.837117307 + 1.5
t = -1.837117307 + 1.5

Combine like terms: -1.837117307 + 1.5 = -0.337117307
t = -0.337117307

Simplifying
t = -0.337117307

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.337117307, -0.337117307}
Solution
t = {3.337117307, -0.337117307}