52=-16t^2+60t+2

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Solution for 52=-16t^2+60t+2 equation: 


Simplifying
52 = -16t2 + 60t + 2

Reorder the terms:
52 = 2 + 60t + -16t2

Solving
52 = 2 + 60t + -16t2

Solving for variable 't'.

Combine like terms: 52 + -2 = 50
50 + -60t + 16t2 = 2 + 60t + -16t2 + -2 + -60t + 16t2

Reorder the terms:
50 + -60t + 16t2 = 2 + -2 + 60t + -60t + -16t2 + 16t2

Combine like terms: 2 + -2 = 0
50 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2
50 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2

Combine like terms: 60t + -60t = 0
50 + -60t + 16t2 = 0 + -16t2 + 16t2
50 + -60t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
50 + -60t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -30t + 8t2) = 0

Factor a trinomial.
2((5 + -4t)(5 + -2t)) = 0

Ignore the factor 2.

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

Simplifying
5 + -4t = 0

Solving
5 + -4t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4t = 0 + -5
-4t = 0 + -5

Combine like terms: 0 + -5 = -5
-4t = -5

Divide each side by '-4'.
t = 1.25

Simplifying
t = 1.25

Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {1.25, 2.5}

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