((T^2+3t-8)-(t^2-2t+6))(t-4)=0

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Solution for ((T^2+3t-8)-(t^2-2t+6))(t-4)=0 equation: 


Simplifying
((T2 + 3t + -8) + -1(t2 + -2t + 6))(t + -4) = 0

Reorder the terms:
((-8 + T2 + 3t) + -1(t2 + -2t + 6))(t + -4) = 0

Remove parenthesis around (-8 + T2 + 3t)
(-8 + T2 + 3t + -1(t2 + -2t + 6))(t + -4) = 0

Reorder the terms:
(-8 + T2 + 3t + -1(6 + -2t + t2))(t + -4) = 0
(-8 + T2 + 3t + (6 * -1 + -2t * -1 + t2 * -1))(t + -4) = 0
(-8 + T2 + 3t + (-6 + 2t + -1t2))(t + -4) = 0

Reorder the terms:
(-8 + -6 + T2 + 3t + 2t + -1t2)(t + -4) = 0

Combine like terms: -8 + -6 = -14
(-14 + T2 + 3t + 2t + -1t2)(t + -4) = 0

Combine like terms: 3t + 2t = 5t
(-14 + T2 + 5t + -1t2)(t + -4) = 0

Reorder the terms:
(-14 + T2 + 5t + -1t2)(-4 + t) = 0

Multiply (-14 + T2 + 5t + -1t2) * (-4 + t)
(-14(-4 + t) + T2(-4 + t) + 5t * (-4 + t) + -1t2 * (-4 + t)) = 0
((-4 * -14 + t * -14) + T2(-4 + t) + 5t * (-4 + t) + -1t2 * (-4 + t)) = 0
((56 + -14t) + T2(-4 + t) + 5t * (-4 + t) + -1t2 * (-4 + t)) = 0
(56 + -14t + (-4 * T2 + t * T2) + 5t * (-4 + t) + -1t2 * (-4 + t)) = 0
(56 + -14t + (-4T2 + tT2) + 5t * (-4 + t) + -1t2 * (-4 + t)) = 0
(56 + -14t + -4T2 + tT2 + (-4 * 5t + t * 5t) + -1t2 * (-4 + t)) = 0
(56 + -14t + -4T2 + tT2 + (-20t + 5t2) + -1t2 * (-4 + t)) = 0
(56 + -14t + -4T2 + tT2 + -20t + 5t2 + (-4 * -1t2 + t * -1t2)) = 0
(56 + -14t + -4T2 + tT2 + -20t + 5t2 + (4t2 + -1t3)) = 0

Reorder the terms:
(56 + -4T2 + -14t + -20t + tT2 + 5t2 + 4t2 + -1t3) = 0

Combine like terms: -14t + -20t = -34t
(56 + -4T2 + -34t + tT2 + 5t2 + 4t2 + -1t3) = 0

Combine like terms: 5t2 + 4t2 = 9t2
(56 + -4T2 + -34t + tT2 + 9t2 + -1t3) = 0

Solving
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 0

Solving for variable 'T'.

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

Add '-56' to each side of the equation.
56 + -4T2 + -34t + tT2 + 9t2 + -56 + -1t3 = 0 + -56

Reorder the terms:
56 + -56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 0 + -56
-4T2 + -34t + tT2 + 9t2 + -1t3 = 0 + -56

Combine like terms: 0 + -56 = -56
-4T2 + -34t + tT2 + 9t2 + -1t3 = -56

Add '34t' to each side of the equation.
-4T2 + -34t + tT2 + 9t2 + 34t + -1t3 = -56 + 34t

Reorder the terms:
-4T2 + -34t + 34t + tT2 + 9t2 + -1t3 = -56 + 34t

Combine like terms: -34t + 34t = 0
-4T2 + 0 + tT2 + 9t2 + -1t3 = -56 + 34t
-4T2 + tT2 + 9t2 + -1t3 = -56 + 34t

Add '-9t2' to each side of the equation.
-4T2 + tT2 + 9t2 + -9t2 + -1t3 = -56 + 34t + -9t2

Combine like terms: 9t2 + -9t2 = 0
-4T2 + tT2 + 0 + -1t3 = -56 + 34t + -9t2
-4T2 + tT2 + -1t3 = -56 + 34t + -9t2

Add 't3' to each side of the equation.
-4T2 + tT2 + -1t3 + t3 = -56 + 34t + -9t2 + t3

Combine like terms: -1t3 + t3 = 0
-4T2 + tT2 + 0 = -56 + 34t + -9t2 + t3
-4T2 + tT2 = -56 + 34t + -9t2 + t3

Reorder the terms:
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = -56 + 34t + -9t2 + t3 + 56 + -34t + 9t2 + -1t3

Reorder the terms:
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = -56 + 56 + 34t + -34t + -9t2 + 9t2 + t3 + -1t3

Combine like terms: -56 + 56 = 0
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 0 + 34t + -34t + -9t2 + 9t2 + t3 + -1t3
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 34t + -34t + -9t2 + 9t2 + t3 + -1t3

Combine like terms: 34t + -34t = 0
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 0 + -9t2 + 9t2 + t3 + -1t3
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = -9t2 + 9t2 + t3 + -1t3

Combine like terms: -9t2 + 9t2 = 0
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 0 + t3 + -1t3
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = t3 + -1t3

Combine like terms: t3 + -1t3 = 0
56 + -4T2 + -34t + tT2 + 9t2 + -1t3 = 0

The solution to this equation could not be determined.

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