(2t^2+t+3)(4t^2+2t-2)=0

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


Simplifying
(2t2 + t + 3)(4t2 + 2t + -2) = 0

Reorder the terms:
(3 + t + 2t2)(4t2 + 2t + -2) = 0

Reorder the terms:
(3 + t + 2t2)(-2 + 2t + 4t2) = 0

Multiply (3 + t + 2t2) * (-2 + 2t + 4t2)
(3(-2 + 2t + 4t2) + t(-2 + 2t + 4t2) + 2t2 * (-2 + 2t + 4t2)) = 0
((-2 * 3 + 2t * 3 + 4t2 * 3) + t(-2 + 2t + 4t2) + 2t2 * (-2 + 2t + 4t2)) = 0
((-6 + 6t + 12t2) + t(-2 + 2t + 4t2) + 2t2 * (-2 + 2t + 4t2)) = 0
(-6 + 6t + 12t2 + (-2 * t + 2t * t + 4t2 * t) + 2t2 * (-2 + 2t + 4t2)) = 0
(-6 + 6t + 12t2 + (-2t + 2t2 + 4t3) + 2t2 * (-2 + 2t + 4t2)) = 0
(-6 + 6t + 12t2 + -2t + 2t2 + 4t3 + (-2 * 2t2 + 2t * 2t2 + 4t2 * 2t2)) = 0
(-6 + 6t + 12t2 + -2t + 2t2 + 4t3 + (-4t2 + 4t3 + 8t4)) = 0

Reorder the terms:
(-6 + 6t + -2t + 12t2 + 2t2 + -4t2 + 4t3 + 4t3 + 8t4) = 0

Combine like terms: 6t + -2t = 4t
(-6 + 4t + 12t2 + 2t2 + -4t2 + 4t3 + 4t3 + 8t4) = 0

Combine like terms: 12t2 + 2t2 = 14t2
(-6 + 4t + 14t2 + -4t2 + 4t3 + 4t3 + 8t4) = 0

Combine like terms: 14t2 + -4t2 = 10t2
(-6 + 4t + 10t2 + 4t3 + 4t3 + 8t4) = 0

Combine like terms: 4t3 + 4t3 = 8t3
(-6 + 4t + 10t2 + 8t3 + 8t4) = 0

Solving
-6 + 4t + 10t2 + 8t3 + 8t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2t + 5t2 + 4t3 + 4t4) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + 2t + 5t2 + 4t3 + 4t4)' equal to zero and attempt to solve:

Simplifying
-3 + 2t + 5t2 + 4t3 + 4t4 = 0

Solving
-3 + 2t + 5t2 + 4t3 + 4t4 = 0

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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