Solve x^3+kx^2+4k-16=-4

$$x ^ { 3 } + k x ^ { 2 } + 4 k - 16 = - 4$$

Solve for k

$$k=-\frac{x^{3}-12}{x^{2}+4}$$

Steps for Solving Linear Equation

Subtract x^{3} from both sides.

$$kx^{2}+4k-16=-4-x^{3}$$

Add 16 to both sides.

$$kx^{2}+4k=-4-x^{3}+16$$

Add -4 and 16 to get 12.

$$kx^{2}+4k=12-x^{3}$$

Combine all terms containing k.

$$\left(x^{2}+4\right)k=12-x^{3}$$

Divide both sides by x^{2}+4.

$$\frac{\left(x^{2}+4\right)k}{x^{2}+4}=\frac{12-x^{3}}{x^{2}+4}$$

Dividing by x^{2}+4 undoes the multiplication by x^{2}+4.

$$k=\frac{12-x^{3}}{x^{2}+4}$$