(t^2+2t)(t^2-2t)=45

Solution for (t^2+2t)(t^2-2t)=45 equation:

Simplifying
(t2 + 2t)(t2 + -2t) = 45

Reorder the terms:
(2t + t2)(t2 + -2t) = 45

Reorder the terms:
(2t + t2)(-2t + t2) = 45

Multiply (2t + t2) * (-2t + t2)
(2t * (-2t + t2) + t2(-2t + t2)) = 45
((-2t * 2t + t2 * 2t) + t2(-2t + t2)) = 45
((-4t2 + 2t3) + t2(-2t + t2)) = 45
(-4t2 + 2t3 + (-2t * t2 + t2 * t2)) = 45
(-4t2 + 2t3 + (-2t3 + t4)) = 45

Combine like terms: 2t3 + -2t3 = 0
(-4t2 + 0 + t4) = 45
(-4t2 + t4) = 45

Solving
-4t2 + t4 = 45

Solving for variable 't'.

Reorder the terms:
-45 + -4t2 + t4 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -4t2 + t4 = 0

Factor a trinomial.
(-5 + -1t2)(9 + -1t2) = 0

Factor a difference between two squares.
(-5 + -1t2)((3 + t)(3 + -1t)) = 0

Subproblem 1
Set the factor '(-5 + -1t2)' equal to zero and attempt to solve:

Simplifying
-5 + -1t2 = 0

Solving
-5 + -1t2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t2 = 0 + 5
-1t2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1t2 = 5

Divide each side by '-1'.
t2 = -5

Simplifying
t2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Subproblem 3
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-3, 3}