9t^4-14t^2+5=0

Solution for 9t^4-14t^2+5=0 equation:

Simplifying
9t4 + -14t2 + 5 = 0

Reorder the terms:
5 + -14t2 + 9t4 = 0

Solving
5 + -14t2 + 9t4 = 0

Solving for variable 't'.

Factor a trinomial.
(5 + -9t2)(1 + -1t2) = 0

Factor a difference between two squares.
(5 + -9t2)((1 + t)(1 + -1t)) = 0

Subproblem 1
Set the factor '(5 + -9t2)' equal to zero and attempt to solve:

Simplifying
5 + -9t2 = 0

Solving
5 + -9t2 = 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 + -9t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9t2 = 0 + -5
-9t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9t2 = -5

Divide each side by '-9'.
t2 = 0.5555555556

Simplifying
t2 = 0.5555555556

Take the square root of each side:
t = {-0.745355993, 0.745355993}
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Subproblem 3
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1t = 0 + -1
-1t = 0 + -1

Combine like terms: 0 + -1 = -1
-1t = -1

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {-0.745355993, 0.745355993, -1, 1}