6x^2=32x^4

Solution for 6x^2=32x^4 equation:

Simplifying
6x2 = 32x4

Solving
6x2 = 32x4

Solving for variable 'x'.

Combine like terms: 32x4 + -32x4 = 0
6x2 + -32x4 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(3 + -16x2) = 0

Ignore the factor 2.
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 '(3 + -16x2)' equal to zero and attempt to solve:

Simplifying
3 + -16x2 = 0

Solving
3 + -16x2 = 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 + -16x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -16x2 = 0 + -3
-16x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-16x2 = -3

Divide each side by '-16'.
x2 = 0.1875

Simplifying
x2 = 0.1875

Take the square root of each side:
x = {-0.433012702, 0.433012702}
Solution
x = {0, -0.433012702, 0.433012702}