t^4+14=9t^2

Solution for t^4+14=9t^2 equation:

Simplifying
t4 + 14 = 9t2

Reorder the terms:
14 + t4 = 9t2

Solving
14 + t4 = 9t2

Solving for variable 't'.

Reorder the terms:
14 + -9t2 + t4 = 9t2 + -9t2

Combine like terms: 9t2 + -9t2 = 0
14 + -9t2 + t4 = 0

Factor a trinomial.
(2 + -1t2)(7 + -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

Take the square root of each side:
t = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(7 + -1t2)' equal to zero and attempt to solve:

Simplifying
7 + -1t2 = 0

Solving
7 + -1t2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t2 = 0 + -7
-1t2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1t2 = -7

Divide each side by '-1'.
t2 = 7

Simplifying
t2 = 7

Take the square root of each side:
t = {-2.645751311, 2.645751311}
Solution
t = {-1.414213562, 1.414213562, -2.645751311, 2.645751311}