x^2(x^2+2)-3(x^2-1)=5*x^2+3

Solution for x^2(x^2+2)-3(x^2-1)=5*x^2+3 equation:

Simplifying
x2(x2 + 2) + -3(x2 + -1) = 5x2 + 3

Reorder the terms:
x2(2 + x2) + -3(x2 + -1) = 5x2 + 3
(2 * x2 + x2 * x2) + -3(x2 + -1) = 5x2 + 3
(2x2 + x4) + -3(x2 + -1) = 5x2 + 3

Reorder the terms:
2x2 + x4 + -3(-1 + x2) = 5x2 + 3
2x2 + x4 + (-1 * -3 + x2 * -3) = 5x2 + 3
2x2 + x4 + (3 + -3x2) = 5x2 + 3

Reorder the terms:
3 + 2x2 + -3x2 + x4 = 5x2 + 3

Combine like terms: 2x2 + -3x2 = -1x2
3 + -1x2 + x4 = 5x2 + 3

Reorder the terms:
3 + -1x2 + x4 = 3 + 5x2

Add '-3' to each side of the equation.
3 + -1x2 + -3 + x4 = 3 + -3 + 5x2

Reorder the terms:
3 + -3 + -1x2 + x4 = 3 + -3 + 5x2

Combine like terms: 3 + -3 = 0
0 + -1x2 + x4 = 3 + -3 + 5x2
-1x2 + x4 = 3 + -3 + 5x2

Combine like terms: 3 + -3 = 0
-1x2 + x4 = 0 + 5x2
-1x2 + x4 = 5x2

Solving
-1x2 + x4 = 5x2

Solving for variable 'x'.

Reorder the terms:
-1x2 + -5x2 + x4 = 5x2 + -5x2

Combine like terms: -1x2 + -5x2 = -6x2
-6x2 + x4 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6x2 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-6 + x2) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(-6 + x2)' equal to zero and attempt to solve:

Simplifying
-6 + x2 = 0

Solving
-6 + x2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x2 = 0 + 6
x2 = 0 + 6

Combine like terms: 0 + 6 = 6
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {0, -2.449489743, 2.449489743}