Solve -3c^{3}*4d^2*10c*2d^4=-240c^4d^6

$$- 3 c ^ { 3 } \times 4 d ^ { 2 } \times 10 c \times 2 d ^ { 4 } = - 240 c ^ { 4 } d ^ { 6 }$$

Solve for c

$$c\in \mathrm{R}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-3c^{4}\times 4d^{2}\times 10\times 2d^{4}=-240c^{4}d^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-3c^{4}\times 4d^{6}\times 10\times 2=-240c^{4}d^{6}$$

Multiply -3 and 4 to get -12.

$$-12c^{4}d^{6}\times 10\times 2=-240c^{4}d^{6}$$

Multiply -12 and 10 to get -120.

$$-120c^{4}d^{6}\times 2=-240c^{4}d^{6}$$

Multiply -120 and 2 to get -240.

$$-240c^{4}d^{6}=-240c^{4}d^{6}$$

Add 240c^{4}d^{6} to both sides.

$$-240c^{4}d^{6}+240c^{4}d^{6}=0$$

Combine -240c^{4}d^{6} and 240c^{4}d^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any c.

$$c\in \mathrm{R}$$

Solve for d

$$d\in \mathrm{R}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-3c^{4}\times 4d^{2}\times 10\times 2d^{4}=-240c^{4}d^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-3c^{4}\times 4d^{6}\times 10\times 2=-240c^{4}d^{6}$$

Multiply -3 and 4 to get -12.

$$-12c^{4}d^{6}\times 10\times 2=-240c^{4}d^{6}$$

Multiply -12 and 10 to get -120.

$$-120c^{4}d^{6}\times 2=-240c^{4}d^{6}$$

Multiply -120 and 2 to get -240.

$$-240c^{4}d^{6}=-240c^{4}d^{6}$$

Add 240c^{4}d^{6} to both sides.

$$-240c^{4}d^{6}+240c^{4}d^{6}=0$$

Combine -240c^{4}d^{6} and 240c^{4}d^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any d.

$$d\in \mathrm{R}$$