t^4+9=t^2+3+12

Solution for t^4+9=t^2+3+12 equation:

Simplifying
t4 + 9 = t2 + 3 + 12

Reorder the terms:
9 + t4 = t2 + 3 + 12

Reorder the terms:
9 + t4 = 3 + 12 + t2

Combine like terms: 3 + 12 = 15
9 + t4 = 15 + t2

Solving
9 + t4 = 15 + t2

Solving for variable 't'.

Reorder the terms:
9 + -15 + -1t2 + t4 = 15 + t2 + -15 + -1t2

Combine like terms: 9 + -15 = -6
-6 + -1t2 + t4 = 15 + t2 + -15 + -1t2

Reorder the terms:
-6 + -1t2 + t4 = 15 + -15 + t2 + -1t2

Combine like terms: 15 + -15 = 0
-6 + -1t2 + t4 = 0 + t2 + -1t2
-6 + -1t2 + t4 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-6 + -1t2 + t4 = 0

Factor a trinomial.
(-2 + -1t2)(3 + -1t2) = 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 '(3 + -1t2)' equal to zero and attempt to solve:

Simplifying
3 + -1t2 = 0

Solving
3 + -1t2 = 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 + -1t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t2 = 0 + -3
-1t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1t2 = -3

Divide each side by '-1'.
t2 = 3

Simplifying
t2 = 3

Take the square root of each side:
t = {-1.732050808, 1.732050808}
Solution
t = {-1.732050808, 1.732050808}