=t^4-18t^2+32

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Solution for =t^4-18t^2+32 equation: 


Simplifying
0 = t4 + -18t2 + 32

Reorder the terms:
0 = 32 + -18t2 + t4

Solving
0 = 32 + -18t2 + t4

Solving for variable 't'.

Combine like terms: 0 + -32 = -32
-32 + 18t2 + -1t4 = 32 + -18t2 + t4 + -32 + 18t2 + -1t4

Reorder the terms:
-32 + 18t2 + -1t4 = 32 + -32 + -18t2 + 18t2 + t4 + -1t4

Combine like terms: 32 + -32 = 0
-32 + 18t2 + -1t4 = 0 + -18t2 + 18t2 + t4 + -1t4
-32 + 18t2 + -1t4 = -18t2 + 18t2 + t4 + -1t4

Combine like terms: -18t2 + 18t2 = 0
-32 + 18t2 + -1t4 = 0 + t4 + -1t4
-32 + 18t2 + -1t4 = t4 + -1t4

Combine like terms: t4 + -1t4 = 0
-32 + 18t2 + -1t4 = 0

Factor a trinomial.
(-16 + t2)(2 + -1t2) = 0

Factor a difference between two squares.
((4 + t)(-4 + t))(2 + -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 '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 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 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4

Subproblem 3
Set the factor '(-4 + t)' equal to zero and attempt to solve:

Simplifying
-4 + t = 0

Solving
-4 + t = 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 + t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + t = 0 + 4
t = 0 + 4

Combine like terms: 0 + 4 = 4
t = 4

Simplifying
t = 4
Solution
t = {-1.414213562, 1.414213562, -4, 4}

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