280=-16t^2+24t+560

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Solution for 280=-16t^2+24t+560 equation: 


Simplifying
280 = -16t2 + 24t + 560

Reorder the terms:
280 = 560 + 24t + -16t2

Solving
280 = 560 + 24t + -16t2

Solving for variable 't'.

Combine like terms: 280 + -560 = -280
-280 + -24t + 16t2 = 560 + 24t + -16t2 + -560 + -24t + 16t2

Reorder the terms:
-280 + -24t + 16t2 = 560 + -560 + 24t + -24t + -16t2 + 16t2

Combine like terms: 560 + -560 = 0
-280 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2
-280 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2

Combine like terms: 24t + -24t = 0
-280 + -24t + 16t2 = 0 + -16t2 + 16t2
-280 + -24t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-280 + -24t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-35 + -3t + 2t2) = 0

Factor a trinomial.
8((-7 + -2t)(5 + -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 '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-3.5, 5}

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