15=3t^2-18t

Solution for 15=3t^2-18t equation:

Simplifying
15 = 3t2 + -18t

Reorder the terms:
15 = -18t + 3t2

Solving
15 = -18t + 3t2

Solving for variable 't'.

Reorder the terms:
15 + 18t + -3t2 = -18t + 18t + 3t2 + -3t2

Combine like terms: -18t + 18t = 0
15 + 18t + -3t2 = 0 + 3t2 + -3t2
15 + 18t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
15 + 18t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 6t + -1t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 6t + -1t2)' equal to zero and attempt to solve:

Simplifying
5 + 6t + -1t2 = 0

Solving
5 + 6t + -1t2 = 0

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

Divide each side by '-1'.
-5 + -6t + t2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -6t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + -6t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6t + t2 = 0 + 5
-6t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
-6t + t2 = 5

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 5 + 9

Reorder the terms:
9 + -6t + t2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + -6t + t2 = 14

Factor a perfect square on the left side:
(t + -3)(t + -3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(t + -3) equal to 3.741657387 and -3.741657387.

Subproblem 1
t + -3 = 3.741657387

Simplifying
t + -3 = 3.741657387

Reorder the terms:
-3 + t = 3.741657387

Solving
-3 + t = 3.741657387

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + t = 3.741657387 + 3
t = 3.741657387 + 3

Combine like terms: 3.741657387 + 3 = 6.741657387
t = 6.741657387

Simplifying
t = 6.741657387

Subproblem 2
t + -3 = -3.741657387

Simplifying
t + -3 = -3.741657387

Reorder the terms:
-3 + t = -3.741657387

Solving
-3 + t = -3.741657387

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + t = -3.741657387 + 3
t = -3.741657387 + 3

Combine like terms: -3.741657387 + 3 = -0.741657387
t = -0.741657387

Simplifying
t = -0.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.741657387, -0.741657387}
Solution
t = {6.741657387, -0.741657387}