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

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

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

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}.

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

Use the distributive property to multiply 2x by 1-x.

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

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

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

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

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

Add 4 and 3 to get 7.

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

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

$$-x^{2}-2x+7=x-x^{2}+6+3$$

Add 6 and 3 to get 9.

$$-x^{2}-2x+7=x-x^{2}+9$$

Subtract x from both sides.

$$-x^{2}-2x+7-x=-x^{2}+9$$

Combine -2x and -x to get -3x.

$$-x^{2}-3x+7=-x^{2}+9$$

Add x^{2} to both sides.

$$-x^{2}-3x+7+x^{2}=9$$

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

$$-3x+7=9$$

Subtract 7 from both sides.

$$-3x=9-7$$

Subtract 7 from 9 to get 2.

$$-3x=2$$

Divide both sides by -3.

$$x=\frac{2}{-3}$$

Fraction \frac{2}{-3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$x=-\frac{2}{3}$$