8x^2=x^3+16x

Solution for 8x^2=x^3+16x equation:

Simplifying
8x2 = x3 + 16x

Reorder the terms:
8x2 = 16x + x3

Solving
8x2 = 16x + x3

Solving for variable 'x'.

Reorder the terms:
-16x + 8x2 + -1x3 = 16x + x3 + -16x + -1x3

Reorder the terms:
-16x + 8x2 + -1x3 = 16x + -16x + x3 + -1x3

Combine like terms: 16x + -16x = 0
-16x + 8x2 + -1x3 = 0 + x3 + -1x3
-16x + 8x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-16x + 8x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-16 + 8x + -1x2) = 0

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 4, 4}