t^2-6t-6t+36=6t-2t^2

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Solution for t^2-6t-6t+36=6t-2t^2 equation: 


Simplifying
t2 + -6t + -6t + 36 = 6t + -2t2

Reorder the terms:
36 + -6t + -6t + t2 = 6t + -2t2

Combine like terms: -6t + -6t = -12t
36 + -12t + t2 = 6t + -2t2

Solving
36 + -12t + t2 = 6t + -2t2

Solving for variable 't'.

Reorder the terms:
36 + -12t + -6t + t2 + 2t2 = 6t + -2t2 + -6t + 2t2

Combine like terms: -12t + -6t = -18t
36 + -18t + t2 + 2t2 = 6t + -2t2 + -6t + 2t2

Combine like terms: t2 + 2t2 = 3t2
36 + -18t + 3t2 = 6t + -2t2 + -6t + 2t2

Reorder the terms:
36 + -18t + 3t2 = 6t + -6t + -2t2 + 2t2

Combine like terms: 6t + -6t = 0
36 + -18t + 3t2 = 0 + -2t2 + 2t2
36 + -18t + 3t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
36 + -18t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -6t + t2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
12 + -6t + t2 = 0

Solving
12 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -6t + -12 + t2 = 0 + -12

Reorder the terms:
12 + -12 + -6t + t2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -6t + t2 = 0 + -12
-6t + t2 = 0 + -12

Combine like terms: 0 + -12 = -12
-6t + t2 = -12

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 = -12 + 9

Reorder the terms:
9 + -6t + t2 = -12 + 9

Combine like terms: -12 + 9 = -3
9 + -6t + t2 = -3

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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