Solve (x+5)(x-5)-(x+3)(x^2-3x+9)=5-x(x^2-x-2)

$$(x+5)(x-5)-(x+3)( { x }^{ 2 } -3x+9)=5-x( { x }^{ 2 } -x-2)$$

Solve for x

$$x = -\frac{57}{2} = -28\frac{1}{2} = -28.5$$

Steps for Solving Linear Equation

Consider \left(x+5\right)\left(x-5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

$$x^{2}-25-\left(x+3\right)\left(x^{2}-3x+9\right)=5-x\left(x^{2}-x-2\right)$$

Use the distributive property to multiply x+3 by x^{2}-3x+9 and combine like terms.

$$x^{2}-25-\left(x^{3}+27\right)=5-x\left(x^{2}-x-2\right)$$

To find the opposite of x^{3}+27, find the opposite of each term.

$$x^{2}-25-x^{3}-27=5-x\left(x^{2}-x-2\right)$$

Subtract 27 from -25 to get -52.

$$x^{2}-52-x^{3}=5-x\left(x^{2}-x-2\right)$$

Use the distributive property to multiply x by x^{2}-x-2.

$$x^{2}-52-x^{3}=5-\left(x^{3}-x^{2}-2x\right)$$

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

$$x^{2}-52-x^{3}=5-x^{3}+x^{2}+2x$$

Add x^{3} to both sides.

$$x^{2}-52-x^{3}+x^{3}=5+x^{2}+2x$$

Combine -x^{3} and x^{3} to get 0.

$$x^{2}-52=5+x^{2}+2x$$

Subtract x^{2} from both sides.

$$x^{2}-52-x^{2}=5+2x$$

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

$$-52=5+2x$$

Swap sides so that all variable terms are on the left hand side.

$$5+2x=-52$$

Subtract 5 from both sides.

$$2x=-52-5$$

Subtract 5 from -52 to get -57.

$$2x=-57$$

Divide both sides by 2.

$$x=\frac{-57}{2}$$

Fraction \frac{-57}{2} can be rewritten as -\frac{57}{2} by extracting the negative sign.

$$x=-\frac{57}{2}$$