9=15t^2+15t

Solution for 9=15t^2+15t equation:

Simplifying
9 = 15t2 + 15t

Reorder the terms:
9 = 15t + 15t2

Solving
9 = 15t + 15t2

Solving for variable 't'.

Reorder the terms:
9 + -15t + -15t2 = 15t + -15t + 15t2 + -15t2

Combine like terms: 15t + -15t = 0
9 + -15t + -15t2 = 0 + 15t2 + -15t2
9 + -15t + -15t2 = 15t2 + -15t2

Combine like terms: 15t2 + -15t2 = 0
9 + -15t + -15t2 = 0

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

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

Simplifying
3 + -5t + -5t2 = 0

Solving
3 + -5t + -5t2 = 0

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

Divide each side by '-5'.
-0.6 + t + t2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + t + 0.6 + t2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + t + t2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + t + t2 = 0 + 0.6
t + t2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
t + t2 = 0.6

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + t2 = 0.6 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
1.25 + t2 = 0.85

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(t + 0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
t + 0.5 = 0.921954446

Simplifying
t + 0.5 = 0.921954446

Reorder the terms:
0.5 + t = 0.921954446

Solving
0.5 + t = 0.921954446

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 0.921954446 + -0.5
t = 0.921954446 + -0.5

Combine like terms: 0.921954446 + -0.5 = 0.421954446
t = 0.421954446

Simplifying
t = 0.421954446

Subproblem 2
t + 0.5 = -0.921954446

Simplifying
t + 0.5 = -0.921954446

Reorder the terms:
0.5 + t = -0.921954446

Solving
0.5 + t = -0.921954446

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -0.921954446 + -0.5
t = -0.921954446 + -0.5

Combine like terms: -0.921954446 + -0.5 = -1.421954446
t = -1.421954446

Simplifying
t = -1.421954446

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.421954446, -1.421954446}
Solution
t = {0.421954446, -1.421954446}