16t^2+48t-36=0

Solution for 16t^2+48t-36=0 equation:

Simplifying
16t2 + 48t + -36 = 0

Reorder the terms:
-36 + 48t + 16t2 = 0

Solving
-36 + 48t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 12t + 4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + 12t + 4t2)' equal to zero and attempt to solve:

Simplifying
-9 + 12t + 4t2 = 0

Solving
-9 + 12t + 4t2 = 0

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

Divide each side by '4'.
-2.25 + 3t + t2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 3t + 2.25 + t2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 3t + t2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 3t + t2 = 0 + 2.25
3t + t2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
3t + t2 = 2.25

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 = 2.25 + 2.25

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

Combine like terms: 2.25 + 2.25 = 4.5
2.25 + 3t + t2 = 4.5

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(t + 1.5) equal to 2.121320344 and -2.121320344.

Subproblem 1
t + 1.5 = 2.121320344

Simplifying
t + 1.5 = 2.121320344

Reorder the terms:
1.5 + t = 2.121320344

Solving
1.5 + t = 2.121320344

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 = 2.121320344 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 2.121320344 + -1.5
t = 2.121320344 + -1.5

Combine like terms: 2.121320344 + -1.5 = 0.621320344
t = 0.621320344

Simplifying
t = 0.621320344

Subproblem 2
t + 1.5 = -2.121320344

Simplifying
t + 1.5 = -2.121320344

Reorder the terms:
1.5 + t = -2.121320344

Solving
1.5 + t = -2.121320344

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 = -2.121320344 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -2.121320344 + -1.5
t = -2.121320344 + -1.5

Combine like terms: -2.121320344 + -1.5 = -3.621320344
t = -3.621320344

Simplifying
t = -3.621320344

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.621320344, -3.621320344}
Solution
t = {0.621320344, -3.621320344}