Solve 03(02x+1)=04(05x-1)

$$03 ( 02 x + 1 ) = 04 ( 05 x - 1 )$$

Solve for x (complex solution)

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

Solution Steps

Multiply 0 and 3 to get 0.

$$0\left(0\times 2x+1\right)=0\times 4\left(0\times 5x-1\right)$$

Multiply 0 and 2 to get 0.

$$0\left(0x+1\right)=0\times 4\left(0\times 5x-1\right)$$

Anything times zero gives zero.

$$0\left(0+1\right)=0\times 4\left(0\times 5x-1\right)$$

Add 0 and 1 to get 1.

$$0\times 1=0\times 4\left(0\times 5x-1\right)$$

Multiply 0 and 1 to get 0.

$$0=0\times 4\left(0\times 5x-1\right)$$

Multiply 0 and 4 to get 0.

$$0=0\left(0\times 5x-1\right)$$

Multiply 0 and 5 to get 0.

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

Anything times zero gives zero.

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

Subtract 1 from 0 to get -1.

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

Multiply 0 and -1 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

Multiply 0 and 3 to get 0.

$$0\left(0\times 2x+1\right)=0\times 4\left(0\times 5x-1\right)$$

Multiply 0 and 2 to get 0.

$$0\left(0x+1\right)=0\times 4\left(0\times 5x-1\right)$$

Anything times zero gives zero.

$$0\left(0+1\right)=0\times 4\left(0\times 5x-1\right)$$

Add 0 and 1 to get 1.

$$0\times 1=0\times 4\left(0\times 5x-1\right)$$

Multiply 0 and 1 to get 0.

$$0=0\times 4\left(0\times 5x-1\right)$$

Multiply 0 and 4 to get 0.

$$0=0\left(0\times 5x-1\right)$$

Multiply 0 and 5 to get 0.

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

Anything times zero gives zero.

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

Subtract 1 from 0 to get -1.

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

Multiply 0 and -1 to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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