0=-16t^2+54t+7

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Solution for 0=-16t^2+54t+7 equation: 


Simplifying
0 = -16t2 + 54t + 7

Reorder the terms:
0 = 7 + 54t + -16t2

Solving
0 = 7 + 54t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -7 = -7
-7 + -54t + 16t2 = 7 + 54t + -16t2 + -7 + -54t + 16t2

Reorder the terms:
-7 + -54t + 16t2 = 7 + -7 + 54t + -54t + -16t2 + 16t2

Combine like terms: 7 + -7 = 0
-7 + -54t + 16t2 = 0 + 54t + -54t + -16t2 + 16t2
-7 + -54t + 16t2 = 54t + -54t + -16t2 + 16t2

Combine like terms: 54t + -54t = 0
-7 + -54t + 16t2 = 0 + -16t2 + 16t2
-7 + -54t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-7 + -54t + 16t2 = 0

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


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

Simplifying
-1 + -8t = 0

Solving
-1 + -8t = 0

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

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

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

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

Divide each side by '-8'.
t = -0.125

Simplifying
t = -0.125

Subproblem 2
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
Solution
t = {-0.125, 3.5}

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