Solve 4-(x-4)^2=12-x^2

$$4 - ( x - 4 ) ^ { 2 } = 12 - x ^ { 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$4-\left(x^{2}-8x+16\right)=12-x^{2}$$

To find the opposite of x^{2}-8x+16, find the opposite of each term.

$$4-x^{2}+8x-16=12-x^{2}$$

Subtract 16 from 4 to get -12.

$$-12-x^{2}+8x=12-x^{2}$$

Add x^{2} to both sides.

$$-12-x^{2}+8x+x^{2}=12$$

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

$$-12+8x=12$$

Add 12 to both sides.

$$8x=12+12$$

Add 12 and 12 to get 24.

$$8x=24$$

Divide both sides by 8.

$$x=\frac{24}{8}$$

Divide 24 by 8 to get 3.

$$x=3$$