0=-16t^2+76t+416

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Solution for 0=-16t^2+76t+416 equation: 


Simplifying
0 = -16t2 + 76t + 416

Reorder the terms:
0 = 416 + 76t + -16t2

Solving
0 = 416 + 76t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -416 = -416
-416 + -76t + 16t2 = 416 + 76t + -16t2 + -416 + -76t + 16t2

Reorder the terms:
-416 + -76t + 16t2 = 416 + -416 + 76t + -76t + -16t2 + 16t2

Combine like terms: 416 + -416 = 0
-416 + -76t + 16t2 = 0 + 76t + -76t + -16t2 + 16t2
-416 + -76t + 16t2 = 76t + -76t + -16t2 + 16t2

Combine like terms: 76t + -76t = 0
-416 + -76t + 16t2 = 0 + -16t2 + 16t2
-416 + -76t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-416 + -76t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-104 + -19t + 4t2) = 0

Factor a trinomial.
4((-13 + -4t)(8 + -1t)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Solution
t = {-3.25, 8}

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