Solve (x-2)^2-2x^2-6=1-(x+1)*(x-3)

$$( x - 2 ) ^ { 2 } - 2 x ^ { 2 } - 6 = 1 - ( x + 1 ) \cdot ( x - 3 )$$

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}.

$$x^{2}-4x+4-2x^{2}-6=1-\left(x+1\right)\left(x-3\right)$$

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

$$-x^{2}-4x+4-6=1-\left(x+1\right)\left(x-3\right)$$

Subtract 6 from 4 to get -2.

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

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

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

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

$$-x^{2}-4x-2=1-x^{2}+2x+3$$

Add 1 and 3 to get 4.

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

Add x^{2} to both sides.

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

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

$$-4x-2=4+2x$$

Subtract 2x from both sides.

$$-4x-2-2x=4$$

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

$$-6x-2=4$$

Add 2 to both sides.

$$-6x=4+2$$

Add 4 and 2 to get 6.

$$-6x=6$$

Divide both sides by -6.

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

Divide 6 by -6 to get -1.

$$x=-1$$