x^2(5x-2)(3x+4)(x+6)=0

Solution for x^2(5x-2)(3x+4)(x+6)=0 equation:

Simplifying
x2(5x + -2)(3x + 4)(x + 6) = 0

Reorder the terms:
x2(-2 + 5x)(3x + 4)(x + 6) = 0

Reorder the terms:
x2(-2 + 5x)(4 + 3x)(x + 6) = 0

Reorder the terms:
x2(-2 + 5x)(4 + 3x)(6 + x) = 0

Multiply (-2 + 5x) * (4 + 3x)
x2(-2(4 + 3x) + 5x * (4 + 3x))(6 + x) = 0
x2((4 * -2 + 3x * -2) + 5x * (4 + 3x))(6 + x) = 0
x2((-8 + -6x) + 5x * (4 + 3x))(6 + x) = 0
x2(-8 + -6x + (4 * 5x + 3x * 5x))(6 + x) = 0
x2(-8 + -6x + (20x + 15x2))(6 + x) = 0

Combine like terms: -6x + 20x = 14x
x2(-8 + 14x + 15x2)(6 + x) = 0

Multiply (-8 + 14x + 15x2) * (6 + x)
x2(-8(6 + x) + 14x * (6 + x) + 15x2 * (6 + x)) = 0
x2((6 * -8 + x * -8) + 14x * (6 + x) + 15x2 * (6 + x)) = 0
x2((-48 + -8x) + 14x * (6 + x) + 15x2 * (6 + x)) = 0
x2(-48 + -8x + (6 * 14x + x * 14x) + 15x2 * (6 + x)) = 0
x2(-48 + -8x + (84x + 14x2) + 15x2 * (6 + x)) = 0
x2(-48 + -8x + 84x + 14x2 + (6 * 15x2 + x * 15x2)) = 0
x2(-48 + -8x + 84x + 14x2 + (90x2 + 15x3)) = 0

Combine like terms: -8x + 84x = 76x
x2(-48 + 76x + 14x2 + 90x2 + 15x3) = 0

Combine like terms: 14x2 + 90x2 = 104x2
x2(-48 + 76x + 104x2 + 15x3) = 0
(-48 * x2 + 76x * x2 + 104x2 * x2 + 15x3 * x2) = 0
(-48x2 + 76x3 + 104x4 + 15x5) = 0

Solving
-48x2 + 76x3 + 104x4 + 15x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-48 + 76x + 104x2 + 15x3) = 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 '(-48 + 76x + 104x2 + 15x3)' equal to zero and attempt to solve:

Simplifying
-48 + 76x + 104x2 + 15x3 = 0

Solving
-48 + 76x + 104x2 + 15x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}