53=-16t^2+56t+40

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Solution for 53=-16t^2+56t+40 equation: 


Simplifying
53 = -16t2 + 56t + 40

Reorder the terms:
53 = 40 + 56t + -16t2

Solving
53 = 40 + 56t + -16t2

Solving for variable 't'.

Combine like terms: 53 + -40 = 13
13 + -56t + 16t2 = 40 + 56t + -16t2 + -40 + -56t + 16t2

Reorder the terms:
13 + -56t + 16t2 = 40 + -40 + 56t + -56t + -16t2 + 16t2

Combine like terms: 40 + -40 = 0
13 + -56t + 16t2 = 0 + 56t + -56t + -16t2 + 16t2
13 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2

Combine like terms: 56t + -56t = 0
13 + -56t + 16t2 = 0 + -16t2 + 16t2
13 + -56t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
13 + -56t + 16t2 = 0

Factor a trinomial.
(1 + -4t)(13 + -4t) = 0


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

Simplifying
1 + -4t = 0

Solving
1 + -4t = 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 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25

Subproblem 2
Set the factor '(13 + -4t)' equal to zero and attempt to solve:

Simplifying
13 + -4t = 0

Solving
13 + -4t = 0

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

Add '-13' to each side of the equation.
13 + -13 + -4t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4t = 0 + -13
-4t = 0 + -13

Combine like terms: 0 + -13 = -13
-4t = -13

Divide each side by '-4'.
t = 3.25

Simplifying
t = 3.25
Solution
t = {0.25, 3.25}

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