288=-16t^2+96t

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Solution for 288=-16t^2+96t equation: 


Simplifying
288 = -16t2 + 96t

Reorder the terms:
288 = 96t + -16t2

Solving
288 = 96t + -16t2

Solving for variable 't'.

Reorder the terms:
288 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
288 + -96t + 16t2 = 0 + -16t2 + 16t2
288 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
288 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(18 + -6t + t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(18 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
18 + -6t + t2 = 0

Solving
18 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -6t + -18 + t2 = 0 + -18

Reorder the terms:
18 + -18 + -6t + t2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -6t + t2 = 0 + -18
-6t + t2 = 0 + -18

Combine like terms: 0 + -18 = -18
-6t + t2 = -18

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -18 + 9

Reorder the terms:
9 + -6t + t2 = -18 + 9

Combine like terms: -18 + 9 = -9
9 + -6t + t2 = -9

Factor a perfect square on the left side:
(t + -3)(t + -3) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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