12t^2-6t+15=0

Solution for 12t^2-6t+15=0 equation:

Simplifying
12t2 + -6t + 15 = 0

Reorder the terms:
15 + -6t + 12t2 = 0

Solving
15 + -6t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -2t + 4t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -2t + 4t2)' equal to zero and attempt to solve:

Simplifying
5 + -2t + 4t2 = 0

Solving
5 + -2t + 4t2 = 0

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

Divide each side by '4'.
1.25 + -0.5t + t2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -0.5t + -1.25 + t2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -0.5t + t2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.5t + t2 = 0 + -1.25
-0.5t + t2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-0.5t + t2 = -1.25

The t term is -0.5t.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5t + 0.0625 + t2 = -1.25 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = -1.25 + 0.0625

Combine like terms: -1.25 + 0.0625 = -1.1875
0.0625 + -0.5t + t2 = -1.1875

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = -1.1875

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.