4t(t-5)-2t(2t+2)+108=3t(2t-5)-t(8t-3)

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Solution for 4t(t-5)-2t(2t+2)+108=3t(2t-5)-t(8t-3) equation: 


Simplifying
4t(t + -5) + -2t(2t + 2) + 108 = 3t(2t + -5) + -1t(8t + -3)

Reorder the terms:
4t(-5 + t) + -2t(2t + 2) + 108 = 3t(2t + -5) + -1t(8t + -3)
(-5 * 4t + t * 4t) + -2t(2t + 2) + 108 = 3t(2t + -5) + -1t(8t + -3)
(-20t + 4t2) + -2t(2t + 2) + 108 = 3t(2t + -5) + -1t(8t + -3)

Reorder the terms:
-20t + 4t2 + -2t(2 + 2t) + 108 = 3t(2t + -5) + -1t(8t + -3)
-20t + 4t2 + (2 * -2t + 2t * -2t) + 108 = 3t(2t + -5) + -1t(8t + -3)
-20t + 4t2 + (-4t + -4t2) + 108 = 3t(2t + -5) + -1t(8t + -3)

Reorder the terms:
108 + -20t + -4t + 4t2 + -4t2 = 3t(2t + -5) + -1t(8t + -3)

Combine like terms: -20t + -4t = -24t
108 + -24t + 4t2 + -4t2 = 3t(2t + -5) + -1t(8t + -3)

Combine like terms: 4t2 + -4t2 = 0
108 + -24t + 0 = 3t(2t + -5) + -1t(8t + -3)
108 + -24t = 3t(2t + -5) + -1t(8t + -3)

Reorder the terms:
108 + -24t = 3t(-5 + 2t) + -1t(8t + -3)
108 + -24t = (-5 * 3t + 2t * 3t) + -1t(8t + -3)
108 + -24t = (-15t + 6t2) + -1t(8t + -3)

Reorder the terms:
108 + -24t = -15t + 6t2 + -1t(-3 + 8t)
108 + -24t = -15t + 6t2 + (-3 * -1t + 8t * -1t)
108 + -24t = -15t + 6t2 + (3t + -8t2)

Reorder the terms:
108 + -24t = -15t + 3t + 6t2 + -8t2

Combine like terms: -15t + 3t = -12t
108 + -24t = -12t + 6t2 + -8t2

Combine like terms: 6t2 + -8t2 = -2t2
108 + -24t = -12t + -2t2

Solving
108 + -24t = -12t + -2t2

Solving for variable 't'.

Combine like terms: -24t + 12t = -12t
108 + -12t + 2t2 = -12t + -2t2 + 12t + 2t2

Reorder the terms:
108 + -12t + 2t2 = -12t + 12t + -2t2 + 2t2

Combine like terms: -12t + 12t = 0
108 + -12t + 2t2 = 0 + -2t2 + 2t2
108 + -12t + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
108 + -12t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(54 + -6t + t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(54 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
54 + -6t + t2 = 0

Solving
54 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -6t + -54 + t2 = 0 + -54

Reorder the terms:
54 + -54 + -6t + t2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -6t + t2 = 0 + -54
-6t + t2 = 0 + -54

Combine like terms: 0 + -54 = -54
-6t + t2 = -54

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 = -54 + 9

Reorder the terms:
9 + -6t + t2 = -54 + 9

Combine like terms: -54 + 9 = -45
9 + -6t + t2 = -45

Factor a perfect square on the left side:
(t + -3)(t + -3) = -45

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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