0=-16t^2+164t-288

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Solution for 0=-16t^2+164t-288 equation: 


Simplifying
0 = -16t2 + 164t + -288

Reorder the terms:
0 = -288 + 164t + -16t2

Solving
0 = -288 + 164t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 288 = 288
288 + -164t + 16t2 = -288 + 164t + -16t2 + 288 + -164t + 16t2

Reorder the terms:
288 + -164t + 16t2 = -288 + 288 + 164t + -164t + -16t2 + 16t2

Combine like terms: -288 + 288 = 0
288 + -164t + 16t2 = 0 + 164t + -164t + -16t2 + 16t2
288 + -164t + 16t2 = 164t + -164t + -16t2 + 16t2

Combine like terms: 164t + -164t = 0
288 + -164t + 16t2 = 0 + -16t2 + 16t2
288 + -164t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
288 + -164t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(72 + -41t + 4t2) = 0

Factor a trinomial.
4((9 + -4t)(8 + -1t)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + -4t)' equal to zero and attempt to solve:

Simplifying
9 + -4t = 0

Solving
9 + -4t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4t = 0 + -9
-4t = 0 + -9

Combine like terms: 0 + -9 = -9
-4t = -9

Divide each side by '-4'.
t = 2.25

Simplifying
t = 2.25

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 = {2.25, 8}

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