60=16t(7-t)

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Solution for 60=16t(7-t) equation: 


Simplifying
60 = 16t(7 + -1t)
60 = (7 * 16t + -1t * 16t)
60 = (112t + -16t2)

Solving
60 = 112t + -16t2

Solving for variable 't'.

Reorder the terms:
60 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2

Combine like terms: 112t + -112t = 0
60 + -112t + 16t2 = 0 + -16t2 + 16t2
60 + -112t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
60 + -112t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -28t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(15 + -28t + 4t2)' equal to zero and attempt to solve:

Simplifying
15 + -28t + 4t2 = 0

Solving
15 + -28t + 4t2 = 0

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

Divide each side by '4'.
3.75 + -7t + t2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -7t + -3.75 + t2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -7t + t2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -7t + t2 = 0 + -3.75
-7t + t2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-7t + t2 = -3.75

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = -3.75 + 12.25

Reorder the terms:
12.25 + -7t + t2 = -3.75 + 12.25

Combine like terms: -3.75 + 12.25 = 8.5
12.25 + -7t + t2 = 8.5

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(t + -3.5) equal to 2.915475947 and -2.915475947.


Subproblem 1
t + -3.5 = 2.915475947

Simplifying
t + -3.5 = 2.915475947

Reorder the terms:
-3.5 + t = 2.915475947

Solving
-3.5 + t = 2.915475947

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 2.915475947 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 2.915475947 + 3.5
t = 2.915475947 + 3.5

Combine like terms: 2.915475947 + 3.5 = 6.415475947
t = 6.415475947

Simplifying
t = 6.415475947


Subproblem 2
t + -3.5 = -2.915475947

Simplifying
t + -3.5 = -2.915475947

Reorder the terms:
-3.5 + t = -2.915475947

Solving
-3.5 + t = -2.915475947

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -2.915475947 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -2.915475947 + 3.5
t = -2.915475947 + 3.5

Combine like terms: -2.915475947 + 3.5 = 0.584524053
t = 0.584524053

Simplifying
t = 0.584524053


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.415475947, 0.584524053}
Solution
t = {6.415475947, 0.584524053}

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