Solve 4x^2-28x+40=4left(x-5right)left(x-2right)

$$4 { x }^{ 2 } -28x+40 = 4 \left( x-5 \right) \left( x-2 \right)$$

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply 4 by x-5.

$$4x^{2}-28x+40=\left(4x-20\right)\left(x-2\right)$$

Use the distributive property to multiply 4x-20 by x-2 and combine like terms.

$$4x^{2}-28x+40=4x^{2}-28x+40$$

Subtract 4x^{2} from both sides.

$$4x^{2}-28x+40-4x^{2}=-28x+40$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-28x+40=-28x+40$$

Add 28x to both sides.

$$-28x+40+28x=40$$

Combine -28x and 28x to get 0.

$$40=40$$

Compare 40 and 40.

$$\text{true}$$

This is true for any x.

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

Solve for x

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

Solution Steps

Use the distributive property to multiply 4 by x-5.

$$4x^{2}-28x+40=\left(4x-20\right)\left(x-2\right)$$

Use the distributive property to multiply 4x-20 by x-2 and combine like terms.

$$4x^{2}-28x+40=4x^{2}-28x+40$$

Subtract 4x^{2} from both sides.

$$4x^{2}-28x+40-4x^{2}=-28x+40$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-28x+40=-28x+40$$

Add 28x to both sides.

$$-28x+40+28x=40$$

Combine -28x and 28x to get 0.

$$40=40$$

Compare 40 and 40.

$$\text{true}$$

This is true for any x.

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