8x^4-47x^3-6x^2=0

Solution for 8x^4-47x^3-6x^2=0 equation:

Simplifying
8x4 + -47x3 + -6x2 = 0

Reorder the terms:
-6x2 + -47x3 + 8x4 = 0

Solving
-6x2 + -47x3 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-6 + -47x + 8x2) = 0

Factor a trinomial.
x2((-1 + -8x)(6 + -1x)) = 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 '(-1 + -8x)' equal to zero and attempt to solve:

Simplifying
-1 + -8x = 0

Solving
-1 + -8x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -8x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x = 0 + 1
-8x = 0 + 1

Combine like terms: 0 + 1 = 1
-8x = 1

Divide each side by '-8'.
x = -0.125

Simplifying
x = -0.125
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

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

Simplifying
x = 6
Solution
x = {0, -0.125, 6}