Solve -2-(x+2)^2=-x+[x*(1-x)-2]

$$- 2 - ( x + 2 ) ^ { 2 } = - x + [ x \cdot ( 1 - x ) - 2 ]$$

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}.

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

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

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

Subtract 4 from -2 to get -6.

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

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

$$-6-x^{2}-4x=-x+x-x^{2}-2$$

Add x to both sides.

$$-6-x^{2}-4x+x=x-x^{2}-2$$

Combine -4x and x to get -3x.

$$-6-x^{2}-3x=x-x^{2}-2$$

Subtract x from both sides.

$$-6-x^{2}-3x-x=-x^{2}-2$$

Combine -3x and -x to get -4x.

$$-6-x^{2}-4x=-x^{2}-2$$

Add x^{2} to both sides.

$$-6-x^{2}-4x+x^{2}=-2$$

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

$$-6-4x=-2$$

Add 6 to both sides.

$$-4x=-2+6$$

Add -2 and 6 to get 4.

$$-4x=4$$

Divide both sides by -4.

$$x=\frac{4}{-4}$$

Divide 4 by -4 to get -1.

$$x=-1$$