16t^2-60t+40=0

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Solution for 16t^2-60t+40=0 equation: 


Simplifying
16t2 + -60t + 40 = 0

Reorder the terms:
40 + -60t + 16t2 = 0

Solving
40 + -60t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + -15t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(10 + -15t + 4t2)' equal to zero and attempt to solve:

Simplifying
10 + -15t + 4t2 = 0

Solving
10 + -15t + 4t2 = 0

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

Divide each side by '4'.
2.5 + -3.75t + t2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -3.75t + -2.5 + t2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -3.75t + t2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -3.75t + t2 = 0 + -2.5
-3.75t + t2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-3.75t + t2 = -2.5

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 = -2.5 + 3.515625

Reorder the terms:
3.515625 + -3.75t + t2 = -2.5 + 3.515625

Combine like terms: -2.5 + 3.515625 = 1.015625
3.515625 + -3.75t + t2 = 1.015625

Factor a perfect square on the left side:
(t + -1.875)(t + -1.875) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(t + -1.875) equal to 1.007782219 and -1.007782219.


Subproblem 1
t + -1.875 = 1.007782219

Simplifying
t + -1.875 = 1.007782219

Reorder the terms:
-1.875 + t = 1.007782219

Solving
-1.875 + t = 1.007782219

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 = 1.007782219 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = 1.007782219 + 1.875
t = 1.007782219 + 1.875

Combine like terms: 1.007782219 + 1.875 = 2.882782219
t = 2.882782219

Simplifying
t = 2.882782219


Subproblem 2
t + -1.875 = -1.007782219

Simplifying
t + -1.875 = -1.007782219

Reorder the terms:
-1.875 + t = -1.007782219

Solving
-1.875 + t = -1.007782219

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 = -1.007782219 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = -1.007782219 + 1.875
t = -1.007782219 + 1.875

Combine like terms: -1.007782219 + 1.875 = 0.867217781
t = 0.867217781

Simplifying
t = 0.867217781


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.882782219, 0.867217781}
Solution
t = {2.882782219, 0.867217781}

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