0=-3t^2+14t-16

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Solution for 0=-3t^2+14t-16 equation: 


Simplifying
0 = -3t2 + 14t + -16

Reorder the terms:
0 = -16 + 14t + -3t2

Solving
0 = -16 + 14t + -3t2

Solving for variable 't'.

Combine like terms: 0 + 16 = 16
16 + -14t + 3t2 = -16 + 14t + -3t2 + 16 + -14t + 3t2

Reorder the terms:
16 + -14t + 3t2 = -16 + 16 + 14t + -14t + -3t2 + 3t2

Combine like terms: -16 + 16 = 0
16 + -14t + 3t2 = 0 + 14t + -14t + -3t2 + 3t2
16 + -14t + 3t2 = 14t + -14t + -3t2 + 3t2

Combine like terms: 14t + -14t = 0
16 + -14t + 3t2 = 0 + -3t2 + 3t2
16 + -14t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
16 + -14t + 3t2 = 0

Factor a trinomial.
(2 + -1t)(8 + -3t) = 0


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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2

Subproblem 2
Set the factor '(8 + -3t)' equal to zero and attempt to solve:

Simplifying
8 + -3t = 0

Solving
8 + -3t = 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 + -3t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3t = 0 + -8
-3t = 0 + -8

Combine like terms: 0 + -8 = -8
-3t = -8

Divide each side by '-3'.
t = 2.666666667

Simplifying
t = 2.666666667
Solution
t = {2, 2.666666667}

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