Solve (x-1)(x-1)-(x-3)(x+7)=10

$$( x - 1 ) ( x - 1 ) - ( x - 3 ) ( x + 7 ) = 10$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply x-1 and x-1 to get \left(x-1\right)^{2}.

$$\left(x-1\right)^{2}-\left(x-3\right)\left(x+7\right)=10$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}-2x+1-\left(x-3\right)\left(x+7\right)=10$$

Use the distributive property to multiply x-3 by x+7 and combine like terms.

$$x^{2}-2x+1-\left(x^{2}+4x-21\right)=10$$

To find the opposite of x^{2}+4x-21, find the opposite of each term.

$$x^{2}-2x+1-x^{2}-4x+21=10$$

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

$$-2x+1-4x+21=10$$

Combine -2x and -4x to get -6x.

$$-6x+1+21=10$$

Add 1 and 21 to get 22.

$$-6x+22=10$$

Subtract 22 from both sides.

$$-6x=10-22$$

Subtract 22 from 10 to get -12.

$$-6x=-12$$

Divide both sides by -6.

$$x=\frac{-12}{-6}$$

Divide -12 by -6 to get 2.

$$x=2$$