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

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

Simplifying
t2(t2 + -4) = 3t2 + -4

Reorder the terms:
t2(-4 + t2) = 3t2 + -4
(-4 * t2 + t2 * t2) = 3t2 + -4
(-4t2 + t4) = 3t2 + -4

Reorder the terms:
-4t2 + t4 = -4 + 3t2

Solving
-4t2 + t4 = -4 + 3t2

Solving for variable 't'.

Reorder the terms:
4 + -4t2 + -3t2 + t4 = -4 + 3t2 + 4 + -3t2

Combine like terms: -4t2 + -3t2 = -7t2
4 + -7t2 + t4 = -4 + 3t2 + 4 + -3t2

Reorder the terms:
4 + -7t2 + t4 = -4 + 4 + 3t2 + -3t2

Combine like terms: -4 + 4 = 0
4 + -7t2 + t4 = 0 + 3t2 + -3t2
4 + -7t2 + t4 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
4 + -7t2 + t4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7t2 + -4 + t4 = 0 + -4

Reorder the terms:
4 + -4 + -7t2 + t4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7t2 + t4 = 0 + -4
-7t2 + t4 = 0 + -4

Combine like terms: 0 + -4 = -4
-7t2 + t4 = -4

The t term is -7t2.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t2 + 12.25 + t4 = -4 + 12.25

Reorder the terms:
12.25 + -7t2 + t4 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + -7t2 + t4 = 8.25

Factor a perfect square on the left side:
(t2 + -3.5)(t2 + -3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(t2 + -3.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
t2 + -3.5 = 2.872281323

Simplifying
t2 + -3.5 = 2.872281323

Reorder the terms:
-3.5 + t2 = 2.872281323

Solving
-3.5 + t2 = 2.872281323

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t2 = 2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t2 = 2.872281323 + 3.5
t2 = 2.872281323 + 3.5

Combine like terms: 2.872281323 + 3.5 = 6.372281323
t2 = 6.372281323

Simplifying
t2 = 6.372281323

Take the square root of each side:
t = {-2.524337799, 2.524337799}

Subproblem 2
t2 + -3.5 = -2.872281323

Simplifying
t2 + -3.5 = -2.872281323

Reorder the terms:
-3.5 + t2 = -2.872281323

Solving
-3.5 + t2 = -2.872281323

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t2 = -2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t2 = -2.872281323 + 3.5
t2 = -2.872281323 + 3.5

Combine like terms: -2.872281323 + 3.5 = 0.627718677
t2 = 0.627718677

Simplifying
t2 = 0.627718677

Take the square root of each side:
t = {-0.792286992, 0.792286992}

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-2.524337799, 2.524337799, -0.792286992, 0.792286992}