x^4+8x^2+12=15x^2

Solution for x^4+8x^2+12=15x^2 equation:

Simplifying
x4 + 8x2 + 12 = 15x2

Reorder the terms:
12 + 8x2 + x4 = 15x2

Solving
12 + 8x2 + x4 = 15x2

Solving for variable 'x'.

Reorder the terms:
12 + 8x2 + -15x2 + x4 = 15x2 + -15x2

Combine like terms: 8x2 + -15x2 = -7x2
12 + -7x2 + x4 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
12 + -7x2 + x4 = 0

Factor a trinomial.
(3 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(3 + -1x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

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

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

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

Simplifying
x = 2
Solution
x = {-1.732050808, 1.732050808, -2, 2}