8x^3=280x^2+288x

Solution for 8x^3=280x^2+288x equation:

Simplifying
8x3 = 280x2 + 288x

Reorder the terms:
8x3 = 288x + 280x2

Solving
8x3 = 288x + 280x2

Solving for variable 'x'.

Reorder the terms:
-288x + -280x2 + 8x3 = 288x + 280x2 + -288x + -280x2

Reorder the terms:
-288x + -280x2 + 8x3 = 288x + -288x + 280x2 + -280x2

Combine like terms: 288x + -288x = 0
-288x + -280x2 + 8x3 = 0 + 280x2 + -280x2
-288x + -280x2 + 8x3 = 280x2 + -280x2

Combine like terms: 280x2 + -280x2 = 0
-288x + -280x2 + 8x3 = 0

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-36 + -35x + x2) = 0

Factor a trinomial.
8x((-1 + -1x)(36 + -1x)) = 0

Ignore the factor 8.
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 '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 3
Set the factor '(36 + -1x)' equal to zero and attempt to solve:

Simplifying
36 + -1x = 0

Solving
36 + -1x = 0

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

Add '-36' to each side of the equation.
36 + -36 + -1x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -1x = 0 + -36
-1x = 0 + -36

Combine like terms: 0 + -36 = -36
-1x = -36

Divide each side by '-1'.
x = 36

Simplifying
x = 36
Solution
x = {0, -1, 36}