6x=7x^2-2x^3

Solution for 6x=7x^2-2x^3 equation:

Simplifying
6x = 7x2 + -2x3

Solving
6x = 7x2 + -2x3

Solving for variable 'x'.

Reorder the terms:
6x + -7x2 + 2x3 = 7x2 + -7x2 + -2x3 + 2x3

Combine like terms: 7x2 + -7x2 = 0
6x + -7x2 + 2x3 = 0 + -2x3 + 2x3
6x + -7x2 + 2x3 = -2x3 + 2x3

Combine like terms: -2x3 + 2x3 = 0
6x + -7x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + -7x + 2x2) = 0

Factor a trinomial.
x((3 + -2x)(2 + -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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 1.5, 2}