15t(t+2)+9t=6

Solution for 15t(t+2)+9t=6 equation:

Simplifying
15t(t + 2) + 9t = 6

Reorder the terms:
15t(2 + t) + 9t = 6
(2 * 15t + t * 15t) + 9t = 6
(30t + 15t2) + 9t = 6

Reorder the terms:
30t + 9t + 15t2 = 6

Combine like terms: 30t + 9t = 39t
39t + 15t2 = 6

Solving
39t + 15t2 = 6

Solving for variable 't'.

Reorder the terms:
-6 + 39t + 15t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 39t + 15t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 13t + 5t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 13t + 5t2)' equal to zero and attempt to solve:

Simplifying
-2 + 13t + 5t2 = 0

Solving
-2 + 13t + 5t2 = 0

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

Divide each side by '5'.
-0.4 + 2.6t + t2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2.6t + 0.4 + t2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2.6t + t2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2.6t + t2 = 0 + 0.4
2.6t + t2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
2.6t + t2 = 0.4

The t term is 2.6t.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6t + 1.69 + t2 = 0.4 + 1.69

Reorder the terms:
1.69 + 2.6t + t2 = 0.4 + 1.69

Combine like terms: 0.4 + 1.69 = 2.09
1.69 + 2.6t + t2 = 2.09

Factor a perfect square on the left side:
(t + 1.3)(t + 1.3) = 2.09

Calculate the square root of the right side: 1.445683229

Break this problem into two subproblems by setting 
(t + 1.3) equal to 1.445683229 and -1.445683229.

Subproblem 1
t + 1.3 = 1.445683229

Simplifying
t + 1.3 = 1.445683229

Reorder the terms:
1.3 + t = 1.445683229

Solving
1.3 + t = 1.445683229

Solving for variable 't'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + t = 1.445683229 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + t = 1.445683229 + -1.3
t = 1.445683229 + -1.3

Combine like terms: 1.445683229 + -1.3 = 0.145683229
t = 0.145683229

Simplifying
t = 0.145683229

Subproblem 2
t + 1.3 = -1.445683229

Simplifying
t + 1.3 = -1.445683229

Reorder the terms:
1.3 + t = -1.445683229

Solving
1.3 + t = -1.445683229

Solving for variable 't'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + t = -1.445683229 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + t = -1.445683229 + -1.3
t = -1.445683229 + -1.3

Combine like terms: -1.445683229 + -1.3 = -2.745683229
t = -2.745683229

Simplifying
t = -2.745683229

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.145683229, -2.745683229}
Solution
t = {0.145683229, -2.745683229}