Solve x^2+6x/2+c/x=0

$$x ^ { 2 } + \frac { 6 x } { 2 } + \frac { c } { x } = 0$$

Solve for c

$$c=-\left(x+3\right)x^{2}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x, the least common multiple of 2,x.

$$2xx^{2}+x\times 6x+2c=0$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x^{3}+x\times 6x+2c=0$$

Multiply x and x to get x^{2}.

$$2x^{3}+x^{2}\times 6+2c=0$$

Subtract 2x^{3} from both sides. Anything subtracted from zero gives its negation.

$$x^{2}\times 6+2c=-2x^{3}$$

Subtract x^{2}\times 6 from both sides.

$$2c=-2x^{3}-x^{2}\times 6$$

Multiply -1 and 6 to get -6.

$$2c=-2x^{3}-6x^{2}$$

Divide both sides by 2.

$$\frac{2c}{2}=-\frac{2\left(x+3\right)x^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$c=-\frac{2\left(x+3\right)x^{2}}{2}$$

Divide -2\left(3+x\right)x^{2} by 2.

$$c=-\left(x+3\right)x^{2}$$