Solve 0=(x-t)*(e^02x-1)

$$0 = ( x - t ) \cdot ( e ^ { 02 x } - 1 )$$

Solve for t (complex solution)

$$t\in \mathrm{C}$$

Solution Steps

Multiply 0 and 2 to get 0.

$$0=\left(x-t\right)\left(e^{0x}-1\right)$$

Anything times zero gives zero.

$$0=\left(x-t\right)\left(e^{0}-1\right)$$

Calculate e to the power of 0 and get 1.

$$0=\left(x-t\right)\left(1-1\right)$$

Subtract 1 from 1 to get 0.

$$0=\left(x-t\right)\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any t.

$$t\in \mathrm{C}$$

Solve for x (complex solution)

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

Solution Steps

Multiply 0 and 2 to get 0.

$$0=\left(x-t\right)\left(e^{0x}-1\right)$$

Anything times zero gives zero.

$$0=\left(x-t\right)\left(e^{0}-1\right)$$

Calculate e to the power of 0 and get 1.

$$0=\left(x-t\right)\left(1-1\right)$$

Subtract 1 from 1 to get 0.

$$0=\left(x-t\right)\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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

Solve for t

$$t\in \mathrm{R}$$

Solution Steps

Multiply 0 and 2 to get 0.

$$0=\left(x-t\right)\left(e^{0x}-1\right)$$

Anything times zero gives zero.

$$0=\left(x-t\right)\left(e^{0}-1\right)$$

Calculate e to the power of 0 and get 1.

$$0=\left(x-t\right)\left(1-1\right)$$

Subtract 1 from 1 to get 0.

$$0=\left(x-t\right)\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any t.

$$t\in \mathrm{R}$$

Solve for x

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

Solution Steps

Multiply 0 and 2 to get 0.

$$0=\left(x-t\right)\left(e^{0x}-1\right)$$

Anything times zero gives zero.

$$0=\left(x-t\right)\left(e^{0}-1\right)$$

Calculate e to the power of 0 and get 1.

$$0=\left(x-t\right)\left(1-1\right)$$

Subtract 1 from 1 to get 0.

$$0=\left(x-t\right)\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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