52=-16t^2+38t+30

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Solution for 52=-16t^2+38t+30 equation: 


Simplifying
52 = -16t2 + 38t + 30

Reorder the terms:
52 = 30 + 38t + -16t2

Solving
52 = 30 + 38t + -16t2

Solving for variable 't'.

Combine like terms: 52 + -30 = 22
22 + -38t + 16t2 = 30 + 38t + -16t2 + -30 + -38t + 16t2

Reorder the terms:
22 + -38t + 16t2 = 30 + -30 + 38t + -38t + -16t2 + 16t2

Combine like terms: 30 + -30 = 0
22 + -38t + 16t2 = 0 + 38t + -38t + -16t2 + 16t2
22 + -38t + 16t2 = 38t + -38t + -16t2 + 16t2

Combine like terms: 38t + -38t = 0
22 + -38t + 16t2 = 0 + -16t2 + 16t2
22 + -38t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
22 + -38t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -19t + 8t2) = 0

Factor a trinomial.
2((1 + -1t)(11 + -8t)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1t = 0 + -1
-1t = 0 + -1

Combine like terms: 0 + -1 = -1
-1t = -1

Divide each side by '-1'.
t = 1

Simplifying
t = 1

Subproblem 2
Set the factor '(11 + -8t)' equal to zero and attempt to solve:

Simplifying
11 + -8t = 0

Solving
11 + -8t = 0

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

Add '-11' to each side of the equation.
11 + -11 + -8t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -8t = 0 + -11
-8t = 0 + -11

Combine like terms: 0 + -11 = -11
-8t = -11

Divide each side by '-8'.
t = 1.375

Simplifying
t = 1.375
Solution
t = {1, 1.375}

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