0=2t^4-21t^2+72-53

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Solution for 0=2t^4-21t^2+72-53 equation: 


Simplifying
0 = 2t4 + -21t2 + 72 + -53

Reorder the terms:
0 = 72 + -53 + -21t2 + 2t4

Combine like terms: 72 + -53 = 19
0 = 19 + -21t2 + 2t4

Solving
0 = 19 + -21t2 + 2t4

Solving for variable 't'.

Combine like terms: 0 + -19 = -19
-19 + 21t2 + -2t4 = 19 + -21t2 + 2t4 + -19 + 21t2 + -2t4

Reorder the terms:
-19 + 21t2 + -2t4 = 19 + -19 + -21t2 + 21t2 + 2t4 + -2t4

Combine like terms: 19 + -19 = 0
-19 + 21t2 + -2t4 = 0 + -21t2 + 21t2 + 2t4 + -2t4
-19 + 21t2 + -2t4 = -21t2 + 21t2 + 2t4 + -2t4

Combine like terms: -21t2 + 21t2 = 0
-19 + 21t2 + -2t4 = 0 + 2t4 + -2t4
-19 + 21t2 + -2t4 = 2t4 + -2t4

Combine like terms: 2t4 + -2t4 = 0
-19 + 21t2 + -2t4 = 0

Factor a trinomial.
(-19 + 2t2)(1 + -1t2) = 0

Factor a difference between two squares.
(-19 + 2t2)((1 + t)(1 + -1t)) = 0


Subproblem 1
Set the factor '(-19 + 2t2)' equal to zero and attempt to solve:

Simplifying
-19 + 2t2 = 0

Solving
-19 + 2t2 = 0

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

Add '19' to each side of the equation.
-19 + 19 + 2t2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2t2 = 0 + 19
2t2 = 0 + 19

Combine like terms: 0 + 19 = 19
2t2 = 19

Divide each side by '2'.
t2 = 9.5

Simplifying
t2 = 9.5

Take the square root of each side:
t = {-3.082207001, 3.082207001}

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 = {-3.082207001, 3.082207001, -1, 1}

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