Solve 4-(x-1)(x-3)=10-x(x-1)

$$4 - ( x - 1 ) ( x - 3 ) = 10 - x ( x - 1 )$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by x-3 and combine like terms.

$$4-\left(x^{2}-4x+3\right)=10-x\left(x-1\right)$$

To find the opposite of x^{2}-4x+3, find the opposite of each term.

$$4-x^{2}+4x-3=10-x\left(x-1\right)$$

Subtract 3 from 4 to get 1.

$$1-x^{2}+4x=10-x\left(x-1\right)$$

Use the distributive property to multiply x by x-1.

$$1-x^{2}+4x=10-\left(x^{2}-x\right)$$

To find the opposite of x^{2}-x, find the opposite of each term.

$$1-x^{2}+4x=10-x^{2}+x$$

Add x^{2} to both sides.

$$1-x^{2}+4x+x^{2}=10+x$$

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

$$1+4x=10+x$$

Subtract x from both sides.

$$1+4x-x=10$$

Combine 4x and -x to get 3x.

$$1+3x=10$$

Subtract 1 from both sides.

$$3x=10-1$$

Subtract 1 from 10 to get 9.

$$3x=9$$

Divide both sides by 3.

$$x=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x=3$$