x^4+0x^3-14x^2+0x+45=0

Solution for x^4+0x^3-14x^2+0x+45=0 equation:

Simplifying
x4 + 0x3 + -14x2 + 0x + 45 = 0

Anything times zero is zero.
x4 + 0x3 + -14x2 + 0x + 45 = 0

Anything times zero is zero.
x4 + 0 + -14x2 + 0x + 45 = 0

Reorder the terms:
0 + 0 + 45 + -14x2 + x4 = 0

Combine like terms: 0 + 0 = 0
0 + 45 + -14x2 + x4 = 0
45 + -14x2 + x4 = 0

Solving
45 + -14x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
(5 + -1x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Solution
x = {-2.236067978, 2.236067978, -3, 3}