-8(t^2+3)(t^2-11)=0

Solution for -8(t^2+3)(t^2-11)=0 equation:

Simplifying
-8(t2 + 3)(t2 + -11) = 0

Reorder the terms:
-8(3 + t2)(t2 + -11) = 0

Reorder the terms:
-8(3 + t2)(-11 + t2) = 0

Multiply (3 + t2) * (-11 + t2)
-8(3(-11 + t2) + t2(-11 + t2)) = 0
-8((-11 * 3 + t2 * 3) + t2(-11 + t2)) = 0
-8((-33 + 3t2) + t2(-11 + t2)) = 0
-8(-33 + 3t2 + (-11 * t2 + t2 * t2)) = 0
-8(-33 + 3t2 + (-11t2 + t4)) = 0

Combine like terms: 3t2 + -11t2 = -8t2
-8(-33 + -8t2 + t4) = 0
(-33 * -8 + -8t2 * -8 + t4 * -8) = 0
(264 + 64t2 + -8t4) = 0

Solving
264 + 64t2 + -8t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(33 + 8t2 + -1t4) = 0

Factor a trinomial.
8((11 + -1t2)(3 + t2)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(11 + -1t2)' equal to zero and attempt to solve:

Simplifying
11 + -1t2 = 0

Solving
11 + -1t2 = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1t2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1t2 = 0 + -11
-1t2 = 0 + -11

Combine like terms: 0 + -11 = -11
-1t2 = -11

Divide each side by '-1'.
t2 = 11

Simplifying
t2 = 11

Take the square root of each side:
t = {-3.31662479, 3.31662479}
Subproblem 2
Set the factor '(3 + t2)' equal to zero and attempt to solve:

Simplifying
3 + t2 = 0

Solving
3 + t2 = 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 + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t2 = 0 + -3
t2 = 0 + -3

Combine like terms: 0 + -3 = -3
t2 = -3

Simplifying
t2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {-3.31662479, 3.31662479}