0=-16t^2+8t+224

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Solution for 0=-16t^2+8t+224 equation: 


Simplifying
0 = -16t2 + 8t + 224

Reorder the terms:
0 = 224 + 8t + -16t2

Solving
0 = 224 + 8t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -224 = -224
-224 + -8t + 16t2 = 224 + 8t + -16t2 + -224 + -8t + 16t2

Reorder the terms:
-224 + -8t + 16t2 = 224 + -224 + 8t + -8t + -16t2 + 16t2

Combine like terms: 224 + -224 = 0
-224 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2
-224 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2

Combine like terms: 8t + -8t = 0
-224 + -8t + 16t2 = 0 + -16t2 + 16t2
-224 + -8t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-224 + -8t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-28 + -1t + 2t2) = 0

Factor a trinomial.
8((-7 + -2t)(4 + -1t)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-7 + -2t)' equal to zero and attempt to solve:

Simplifying
-7 + -2t = 0

Solving
-7 + -2t = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2t = 0 + 7
-2t = 0 + 7

Combine like terms: 0 + 7 = 7
-2t = 7

Divide each side by '-2'.
t = -3.5

Simplifying
t = -3.5

Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-3.5, 4}

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