Solve 2x^2*3x^4=6x^6

$$2 { x }^{ 2 } \times 3 { x }^{ 4 } =6 { x }^{ 6 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

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

$$2x^{6}\times 3=6x^{6}$$

Multiply 2 and 3 to get 6.

$$6x^{6}=6x^{6}$$

Subtract 6x^{6} from both sides.

$$6x^{6}-6x^{6}=0$$

Combine 6x^{6} and -6x^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

$$2x^{6}\times 3=6x^{6}$$

Multiply 2 and 3 to get 6.

$$6x^{6}=6x^{6}$$

Subtract 6x^{6} from both sides.

$$6x^{6}-6x^{6}=0$$

Combine 6x^{6} and -6x^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$