5x^2(x^2-6)=0

Solution for 5x^2(x^2-6)=0 equation:

Simplifying
5x2(x2 + -6) = 0

Reorder the terms:
5x2(-6 + x2) = 0
(-6 * 5x2 + x2 * 5x2) = 0
(-30x2 + 5x4) = 0

Solving
-30x2 + 5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(-6 + x2) = 0

Ignore the factor 5.
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}