Solve 0=m(x^2-16c+48)

$$0 = m ( x ^ { 2 } - 16 c + 48 )$$

Solve for c (complex solution)

$$\left\{\begin{matrix}\\c=\frac{x^{2}+48}{16}\text{, }&\text{unconditionally}\\c\in \mathrm{C}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x^{2}-16c+48.

$$0=mx^{2}-16mc+48m$$

Swap sides so that all variable terms are on the left hand side.

$$mx^{2}-16mc+48m=0$$

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

$$-16mc+48m=-mx^{2}$$

Subtract 48m from both sides.

$$-16mc=-mx^{2}-48m$$

Reorder the terms.

$$-16cm=-mx^{2}-48m$$

The equation is in standard form.

$$\left(-16m\right)c=-mx^{2}-48m$$

Divide both sides by -16m.

$$\frac{\left(-16m\right)c}{-16m}=-\frac{m\left(x^{2}+48\right)}{-16m}$$

Dividing by -16m undoes the multiplication by -16m.

$$c=-\frac{m\left(x^{2}+48\right)}{-16m}$$

Divide -m\left(x^{2}+48\right) by -16m.

$$c=\frac{x^{2}}{16}+3$$

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&c=\frac{x^{2}}{16}+3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x^{2}-16c+48.

$$0=mx^{2}-16mc+48m$$

Swap sides so that all variable terms are on the left hand side.

$$mx^{2}-16mc+48m=0$$

Combine all terms containing m.

$$\left(x^{2}-16c+48\right)m=0$$

Divide 0 by x^{2}-16c+48.

$$m=0$$

Solve for c

$$\left\{\begin{matrix}\\c=\frac{x^{2}+48}{16}\text{, }&\text{unconditionally}\\c\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x^{2}-16c+48.

$$0=mx^{2}-16mc+48m$$

Swap sides so that all variable terms are on the left hand side.

$$mx^{2}-16mc+48m=0$$

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

$$-16mc+48m=-mx^{2}$$

Subtract 48m from both sides.

$$-16mc=-mx^{2}-48m$$

Reorder the terms.

$$-16cm=-mx^{2}-48m$$

The equation is in standard form.

$$\left(-16m\right)c=-mx^{2}-48m$$

Divide both sides by -16m.

$$\frac{\left(-16m\right)c}{-16m}=-\frac{m\left(x^{2}+48\right)}{-16m}$$

Dividing by -16m undoes the multiplication by -16m.

$$c=-\frac{m\left(x^{2}+48\right)}{-16m}$$

Divide -m\left(x^{2}+48\right) by -16m.

$$c=\frac{x^{2}}{16}+3$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&c=\frac{x^{2}}{16}+3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x^{2}-16c+48.

$$0=mx^{2}-16mc+48m$$

Swap sides so that all variable terms are on the left hand side.

$$mx^{2}-16mc+48m=0$$

Combine all terms containing m.

$$\left(x^{2}-16c+48\right)m=0$$

Divide 0 by x^{2}-16c+48.

$$m=0$$