16(t^2-12t+10)=0

Solution for 16(t^2-12t+10)=0 equation:

Simplifying
16(t2 + -12t + 10) = 0

Reorder the terms:
16(10 + -12t + t2) = 0
(10 * 16 + -12t * 16 + t2 * 16) = 0
(160 + -192t + 16t2) = 0

Solving
160 + -192t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(10 + -12t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(10 + -12t + t2)' equal to zero and attempt to solve:

Simplifying
10 + -12t + t2 = 0

Solving
10 + -12t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -12t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + -12t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -12t + t2 = 0 + -10
-12t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
-12t + t2 = -10

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = -10 + 36

Reorder the terms:
36 + -12t + t2 = -10 + 36

Combine like terms: -10 + 36 = 26
36 + -12t + t2 = 26

Factor a perfect square on the left side:
(t + -6)(t + -6) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(t + -6) equal to 5.099019514 and -5.099019514.

Subproblem 1
t + -6 = 5.099019514

Simplifying
t + -6 = 5.099019514

Reorder the terms:
-6 + t = 5.099019514

Solving
-6 + t = 5.099019514

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = 5.099019514 + 6

Combine like terms: -6 + 6 = 0
0 + t = 5.099019514 + 6
t = 5.099019514 + 6

Combine like terms: 5.099019514 + 6 = 11.099019514
t = 11.099019514

Simplifying
t = 11.099019514

Subproblem 2
t + -6 = -5.099019514

Simplifying
t + -6 = -5.099019514

Reorder the terms:
-6 + t = -5.099019514

Solving
-6 + t = -5.099019514

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = -5.099019514 + 6

Combine like terms: -6 + 6 = 0
0 + t = -5.099019514 + 6
t = -5.099019514 + 6

Combine like terms: -5.099019514 + 6 = 0.900980486
t = 0.900980486

Simplifying
t = 0.900980486

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.099019514, 0.900980486}
Solution
t = {11.099019514, 0.900980486}