Solve x^3+6570x^2-n39950*(500-x)=0

$$x ^ { 3 } + 6570 x ^ { 2 } - n 39950 \times ( 500 - x ) = 0$$

Solve for n_39950

$$n_{39950}=-\frac{\left(x+6570\right)x^{2}}{x-500}$$

$$x\neq 500$$

Steps for Solving Linear Equation

Use the distributive property to multiply n_{39950} by 500-x.

$$x^{3}+6570x^{2}-\left(500n_{39950}-n_{39950}x\right)=0$$

To find the opposite of 500n_{39950}-n_{39950}x, find the opposite of each term.

$$x^{3}+6570x^{2}-500n_{39950}+n_{39950}x=0$$

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

$$6570x^{2}-500n_{39950}+n_{39950}x=-x^{3}$$

Subtract 6570x^{2} from both sides.

$$-500n_{39950}+n_{39950}x=-x^{3}-6570x^{2}$$

Combine all terms containing n_{39950}.

$$\left(-500+x\right)n_{39950}=-x^{3}-6570x^{2}$$

The equation is in standard form.

$$\left(x-500\right)n_{39950}=-x^{3}-6570x^{2}$$

Divide both sides by x-500.

$$\frac{\left(x-500\right)n_{39950}}{x-500}=-\frac{\left(x+6570\right)x^{2}}{x-500}$$

Dividing by x-500 undoes the multiplication by x-500.

$$n_{39950}=-\frac{\left(x+6570\right)x^{2}}{x-500}$$