(x^2+2x+3)(x^2-2x+3)=17

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Solution for (x^2+2x+3)(x^2-2x+3)=17 equation: 


Simplifying
(x2 + 2x + 3)(x2 + -2x + 3) = 17

Reorder the terms:
(3 + 2x + x2)(x2 + -2x + 3) = 17

Reorder the terms:
(3 + 2x + x2)(3 + -2x + x2) = 17

Multiply (3 + 2x + x2) * (3 + -2x + x2)
(3(3 + -2x + x2) + 2x * (3 + -2x + x2) + x2(3 + -2x + x2)) = 17
((3 * 3 + -2x * 3 + x2 * 3) + 2x * (3 + -2x + x2) + x2(3 + -2x + x2)) = 17
((9 + -6x + 3x2) + 2x * (3 + -2x + x2) + x2(3 + -2x + x2)) = 17
(9 + -6x + 3x2 + (3 * 2x + -2x * 2x + x2 * 2x) + x2(3 + -2x + x2)) = 17
(9 + -6x + 3x2 + (6x + -4x2 + 2x3) + x2(3 + -2x + x2)) = 17
(9 + -6x + 3x2 + 6x + -4x2 + 2x3 + (3 * x2 + -2x * x2 + x2 * x2)) = 17
(9 + -6x + 3x2 + 6x + -4x2 + 2x3 + (3x2 + -2x3 + x4)) = 17

Reorder the terms:
(9 + -6x + 6x + 3x2 + -4x2 + 3x2 + 2x3 + -2x3 + x4) = 17

Combine like terms: -6x + 6x = 0
(9 + 0 + 3x2 + -4x2 + 3x2 + 2x3 + -2x3 + x4) = 17
(9 + 3x2 + -4x2 + 3x2 + 2x3 + -2x3 + x4) = 17

Combine like terms: 3x2 + -4x2 = -1x2
(9 + -1x2 + 3x2 + 2x3 + -2x3 + x4) = 17

Combine like terms: -1x2 + 3x2 = 2x2
(9 + 2x2 + 2x3 + -2x3 + x4) = 17

Combine like terms: 2x3 + -2x3 = 0
(9 + 2x2 + 0 + x4) = 17
(9 + 2x2 + x4) = 17

Solving
9 + 2x2 + x4 = 17

Solving for variable 'x'.

Reorder the terms:
9 + -17 + 2x2 + x4 = 17 + -17

Combine like terms: 9 + -17 = -8
-8 + 2x2 + x4 = 17 + -17

Combine like terms: 17 + -17 = 0
-8 + 2x2 + x4 = 0

Factor a trinomial.
(-4 + -1x2)(2 + -1x2) = 0


Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x2 = 0

Solving
-4 + -1x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x2 = 0 + 4
-1x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x2 = 4

Divide each side by '-1'.
x2 = -4

Simplifying
x2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

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

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