10(6-x^2)=x^2(6-x^2)

Solution for 10(6-x^2)=x^2(6-x^2) equation:

Simplifying
10(6 + -1x2) = x2(6 + -1x2)
(6 * 10 + -1x2 * 10) = x2(6 + -1x2)
(60 + -10x2) = x2(6 + -1x2)
60 + -10x2 = (6 * x2 + -1x2 * x2)
60 + -10x2 = (6x2 + -1x4)

Solving
60 + -10x2 = 6x2 + -1x4

Solving for variable 'x'.

Combine like terms: -10x2 + -6x2 = -16x2
60 + -16x2 + x4 = 6x2 + -1x4 + -6x2 + x4

Reorder the terms:
60 + -16x2 + x4 = 6x2 + -6x2 + -1x4 + x4

Combine like terms: 6x2 + -6x2 = 0
60 + -16x2 + x4 = 0 + -1x4 + x4
60 + -16x2 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
60 + -16x2 + x4 = 0

Factor a trinomial.
(6 + -1x2)(10 + -1x2) = 0

Subproblem 1
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 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 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Subproblem 2
Set the factor '(10 + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + -1x2 = 0

Solving
10 + -1x2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x2 = 0 + -10
-1x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1x2 = -10

Divide each side by '-1'.
x2 = 10

Simplifying
x2 = 10

Take the square root of each side:
x = {-3.16227766, 3.16227766}
Solution
x = {-2.449489743, 2.449489743, -3.16227766, 3.16227766}