15=16t^2+32t+18

Solution for 15=16t^2+32t+18 equation:

Simplifying
15 = 16t2 + 32t + 18

Reorder the terms:
15 = 18 + 32t + 16t2

Solving
15 = 18 + 32t + 16t2

Solving for variable 't'.

Combine like terms: 15 + -18 = -3
-3 + -32t + -16t2 = 18 + 32t + 16t2 + -18 + -32t + -16t2

Reorder the terms:
-3 + -32t + -16t2 = 18 + -18 + 32t + -32t + 16t2 + -16t2

Combine like terms: 18 + -18 = 0
-3 + -32t + -16t2 = 0 + 32t + -32t + 16t2 + -16t2
-3 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
-3 + -32t + -16t2 = 0 + 16t2 + -16t2
-3 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-3 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 32t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 32t + 16t2)' equal to zero and attempt to solve:

Simplifying
3 + 32t + 16t2 = 0

Solving
3 + 32t + 16t2 = 0

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

Divide each side by '16'.
0.1875 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + 2t + -0.1875 + t2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + 2t + t2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + 2t + t2 = 0 + -0.1875
2t + t2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
2t + t2 = -0.1875

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = -0.1875 + 1

Reorder the terms:
1 + 2t + t2 = -0.1875 + 1

Combine like terms: -0.1875 + 1 = 0.8125
1 + 2t + t2 = 0.8125

Factor a perfect square on the left side:
(t + 1)(t + 1) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(t + 1) equal to 0.901387819 and -0.901387819.

Subproblem 1
t + 1 = 0.901387819

Simplifying
t + 1 = 0.901387819

Reorder the terms:
1 + t = 0.901387819

Solving
1 + t = 0.901387819

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 0.901387819 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.901387819 + -1
t = 0.901387819 + -1

Combine like terms: 0.901387819 + -1 = -0.098612181
t = -0.098612181

Simplifying
t = -0.098612181

Subproblem 2
t + 1 = -0.901387819

Simplifying
t + 1 = -0.901387819

Reorder the terms:
1 + t = -0.901387819

Solving
1 + t = -0.901387819

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -0.901387819 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.901387819 + -1
t = -0.901387819 + -1

Combine like terms: -0.901387819 + -1 = -1.901387819
t = -1.901387819

Simplifying
t = -1.901387819

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.098612181, -1.901387819}
Solution
t = {-0.098612181, -1.901387819}