6=t^2+9t

Solution for 6=t^2+9t equation:

Simplifying
6 = t2 + 9t

Reorder the terms:
6 = 9t + t2

Solving
6 = 9t + t2

Solving for variable 't'.

Reorder the terms:
6 + -9t + -1t2 = 9t + -9t + t2 + -1t2

Combine like terms: 9t + -9t = 0
6 + -9t + -1t2 = 0 + t2 + -1t2
6 + -9t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
6 + -9t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 9t + t2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 9t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + 9t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 9t + t2 = 0 + 6
9t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
9t + t2 = 6

The t term is 9t.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9t + 20.25 + t2 = 6 + 20.25

Reorder the terms:
20.25 + 9t + t2 = 6 + 20.25

Combine like terms: 6 + 20.25 = 26.25
20.25 + 9t + t2 = 26.25

Factor a perfect square on the left side:
(t + 4.5)(t + 4.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(t + 4.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
t + 4.5 = 5.123475383

Simplifying
t + 4.5 = 5.123475383

Reorder the terms:
4.5 + t = 5.123475383

Solving
4.5 + t = 5.123475383

Solving for variable 't'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + t = 5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + t = 5.123475383 + -4.5
t = 5.123475383 + -4.5

Combine like terms: 5.123475383 + -4.5 = 0.623475383
t = 0.623475383

Simplifying
t = 0.623475383

Subproblem 2
t + 4.5 = -5.123475383

Simplifying
t + 4.5 = -5.123475383

Reorder the terms:
4.5 + t = -5.123475383

Solving
4.5 + t = -5.123475383

Solving for variable 't'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + t = -5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + t = -5.123475383 + -4.5
t = -5.123475383 + -4.5

Combine like terms: -5.123475383 + -4.5 = -9.623475383
t = -9.623475383

Simplifying
t = -9.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.623475383, -9.623475383}