Solve (x+2)^2-(x+4)(x-2)+10=(3-x)(5-x)-(x-1)^2

$$( x + 2 ) ^ { 2 } - ( x + 4 ) ( x - 2 ) + 10 = ( 3 - x ) ( 5 - x ) - ( x - 1 ) ^ { 2 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

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

$$x^{2}+4x+4-\left(x+4\right)\left(x-2\right)+10=\left(3-x\right)\left(5-x\right)-\left(x-1\right)^{2}$$

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

$$x^{2}+4x+4-\left(x^{2}+2x-8\right)+10=\left(3-x\right)\left(5-x\right)-\left(x-1\right)^{2}$$

To find the opposite of x^{2}+2x-8, find the opposite of each term.

$$x^{2}+4x+4-x^{2}-2x+8+10=\left(3-x\right)\left(5-x\right)-\left(x-1\right)^{2}$$

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

$$4x+4-2x+8+10=\left(3-x\right)\left(5-x\right)-\left(x-1\right)^{2}$$

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

$$2x+4+8+10=\left(3-x\right)\left(5-x\right)-\left(x-1\right)^{2}$$

Add 4 and 8 to get 12.

$$2x+12+10=\left(3-x\right)\left(5-x\right)-\left(x-1\right)^{2}$$

Add 12 and 10 to get 22.

$$2x+22=\left(3-x\right)\left(5-x\right)-\left(x-1\right)^{2}$$

Use the distributive property to multiply 3-x by 5-x and combine like terms.

$$2x+22=15-8x+x^{2}-\left(x-1\right)^{2}$$

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

$$2x+22=15-8x+x^{2}-\left(x^{2}-2x+1\right)$$

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$2x+22=15-8x+x^{2}-x^{2}+2x-1$$

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

$$2x+22=15-8x+2x-1$$

Combine -8x and 2x to get -6x.

$$2x+22=15-6x-1$$

Subtract 1 from 15 to get 14.

$$2x+22=14-6x$$

Add 6x to both sides.

$$2x+22+6x=14$$

Combine 2x and 6x to get 8x.

$$8x+22=14$$

Subtract 22 from both sides.

$$8x=14-22$$

Subtract 22 from 14 to get -8.

$$8x=-8$$

Divide both sides by 8.

$$x=\frac{-8}{8}$$

Divide -8 by 8 to get -1.

$$x=-1$$