4t^2-15t+12=0

Solution for 4t^2-15t+12=0 equation:

Simplifying
4t2 + -15t + 12 = 0

Reorder the terms:
12 + -15t + 4t2 = 0

Solving
12 + -15t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
3 + -3.75t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3.75t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -3.75t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -3.75t + t2 = 0 + -3
-3.75t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-3.75t + t2 = -3

The t term is -3.75t.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75t + 3.515625 + t2 = -3 + 3.515625

Reorder the terms:
3.515625 + -3.75t + t2 = -3 + 3.515625

Combine like terms: -3 + 3.515625 = 0.515625
3.515625 + -3.75t + t2 = 0.515625

Factor a perfect square on the left side:
(t + -1.875)(t + -1.875) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(t + -1.875) equal to 0.718070331 and -0.718070331.

Subproblem 1
t + -1.875 = 0.718070331

Simplifying
t + -1.875 = 0.718070331

Reorder the terms:
-1.875 + t = 0.718070331

Solving
-1.875 + t = 0.718070331

Solving for variable 't'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + t = 0.718070331 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = 0.718070331 + 1.875
t = 0.718070331 + 1.875

Combine like terms: 0.718070331 + 1.875 = 2.593070331
t = 2.593070331

Simplifying
t = 2.593070331

Subproblem 2
t + -1.875 = -0.718070331

Simplifying
t + -1.875 = -0.718070331

Reorder the terms:
-1.875 + t = -0.718070331

Solving
-1.875 + t = -0.718070331

Solving for variable 't'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + t = -0.718070331 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = -0.718070331 + 1.875
t = -0.718070331 + 1.875

Combine like terms: -0.718070331 + 1.875 = 1.156929669
t = 1.156929669

Simplifying
t = 1.156929669

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.593070331, 1.156929669}