6x=2x^3+11x^2

Solution for 6x=2x^3+11x^2 equation:

Simplifying
6x = 2x3 + 11x2

Reorder the terms:
6x = 11x2 + 2x3

Solving
6x = 11x2 + 2x3

Solving for variable 'x'.

Reorder the terms:
6x + -11x2 + -2x3 = 11x2 + -11x2 + 2x3 + -2x3

Combine like terms: 11x2 + -11x2 = 0
6x + -11x2 + -2x3 = 0 + 2x3 + -2x3
6x + -11x2 + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
6x + -11x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + -11x + -2x2) = 0

Factor a trinomial.
x((1 + -2x)(6 + x)) = 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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

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

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

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

Simplifying
x = -6
Solution
x = {0, 0.5, -6}