3t^4=-2t^2+8

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Solution for 3t^4=-2t^2+8 equation: 


Simplifying
3t4 = -2t2 + 8

Reorder the terms:
3t4 = 8 + -2t2

Solving
3t4 = 8 + -2t2

Solving for variable 't'.

Reorder the terms:
-8 + 2t2 + 3t4 = 8 + -2t2 + -8 + 2t2

Reorder the terms:
-8 + 2t2 + 3t4 = 8 + -8 + -2t2 + 2t2

Combine like terms: 8 + -8 = 0
-8 + 2t2 + 3t4 = 0 + -2t2 + 2t2
-8 + 2t2 + 3t4 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
-8 + 2t2 + 3t4 = 0

Factor a trinomial.
(-2 + -1t2)(4 + -3t2) = 0


Subproblem 1
Set the factor '(-2 + -1t2)' equal to zero and attempt to solve:

Simplifying
-2 + -1t2 = 0

Solving
-2 + -1t2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t2 = 0 + 2
-1t2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1t2 = 2

Divide each side by '-1'.
t2 = -2

Simplifying
t2 = -2

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 '(4 + -3t2)' equal to zero and attempt to solve:

Simplifying
4 + -3t2 = 0

Solving
4 + -3t2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3t2 = 0 + -4

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

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

Divide each side by '-3'.
t2 = 1.333333333

Simplifying
t2 = 1.333333333

Take the square root of each side:
t = {-1.154700538, 1.154700538}
Solution
t = {-1.154700538, 1.154700538}

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