(3t^2-8)(t^2+5)=

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Solution for (3t^2-8)(t^2+5)= equation: 


Simplifying
(3t2 + -8)(t2 + 5) = 0

Reorder the terms:
(-8 + 3t2)(t2 + 5) = 0

Reorder the terms:
(-8 + 3t2)(5 + t2) = 0

Multiply (-8 + 3t2) * (5 + t2)
(-8(5 + t2) + 3t2 * (5 + t2)) = 0
((5 * -8 + t2 * -8) + 3t2 * (5 + t2)) = 0
((-40 + -8t2) + 3t2 * (5 + t2)) = 0
(-40 + -8t2 + (5 * 3t2 + t2 * 3t2)) = 0
(-40 + -8t2 + (15t2 + 3t4)) = 0

Combine like terms: -8t2 + 15t2 = 7t2
(-40 + 7t2 + 3t4) = 0

Solving
-40 + 7t2 + 3t4 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -1t2)(8 + -3t2) = 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 '(8 + -3t2)' equal to zero and attempt to solve:

Simplifying
8 + -3t2 = 0

Solving
8 + -3t2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3t2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3t2 = 0 + -8
-3t2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3t2 = -8

Divide each side by '-3'.
t2 = 2.666666667

Simplifying
t2 = 2.666666667

Take the square root of each side:
t = {-1.632993162, 1.632993162}
Solution
t = {-1.632993162, 1.632993162}

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