Solve c=2m+5m^2-3c+2x^2-15x+9+7x^3-19

$$c = 2 m + 5 m ^ { 2 } - 3 c + 2 x ^ { 2 } - 15 x + 9 + 7 x ^ { 3 } - 19$$

Solve for c

$$c=\frac{7x^{3}}{4}+\frac{5m^{2}}{4}+\frac{x^{2}}{2}+\frac{m}{2}-\frac{15x}{4}-\frac{5}{2}$$

Steps for Solving Linear Equation

Subtract 19 from 9 to get -10.

$$c=2m+5m^{2}-3c+2x^{2}-15x-10+7x^{3}$$

Add 3c to both sides.

$$c+3c=2m+5m^{2}+2x^{2}-15x-10+7x^{3}$$

Combine c and 3c to get 4c.

$$4c=2m+5m^{2}+2x^{2}-15x-10+7x^{3}$$

The equation is in standard form.

$$4c=7x^{3}+2x^{2}-15x+5m^{2}+2m-10$$

Divide both sides by 4.

$$\frac{4c}{4}=\frac{7x^{3}+2x^{2}-15x+5m^{2}+2m-10}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$c=\frac{7x^{3}+2x^{2}-15x+5m^{2}+2m-10}{4}$$

Divide 2m+5m^{2}+2x^{2}-15x-10+7x^{3} by 4.

$$c=\frac{7x^{3}}{4}+\frac{5m^{2}}{4}+\frac{x^{2}}{2}+\frac{m}{2}-\frac{15x}{4}-\frac{5}{2}$$

Solve for m

$$m=\frac{\sqrt{51+20c+75x-10x^{2}-35x^{3}}-1}{5}$$

$$m=\frac{-\sqrt{51+20c+75x-10x^{2}-35x^{3}}-1}{5}\text{, }c\geq \frac{7x^{3}}{4}+\frac{x^{2}}{2}-\frac{15x}{4}-\frac{51}{20}$$