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

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

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

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

Reorder the terms:
4t + t2 + t(-2 + 4t2) = 0
4t + t2 + (-2 * t + 4t2 * t) = 0
4t + t2 + (-2t + 4t3) = 0

Reorder the terms:
4t + -2t + t2 + 4t3 = 0

Combine like terms: 4t + -2t = 2t
2t + t2 + 4t3 = 0

Solving
2t + t2 + 4t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(2 + t + 4t2) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(2 + t + 4t2)' equal to zero and attempt to solve:

Simplifying
2 + t + 4t2 = 0

Solving
2 + t + 4t2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.5 + 0.25t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.25t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.25t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.25t + t2 = 0 + -0.5
0.25t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.25t + t2 = -0.5

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25t + 0.25 + t2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.25t + t2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.25t + t2 = -0.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -0.25

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.
Solution
t = {0}