Solve (x-2)(4-x)=6-x^2

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

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by 4-x and combine like terms.

$$6x-x^{2}-8=6-x^{2}$$

Add x^{2} to both sides.

$$6x-x^{2}-8+x^{2}=6$$

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

$$6x-8=6$$

Add 8 to both sides.

$$6x=6+8$$

Add 6 and 8 to get 14.

$$6x=14$$

Divide both sides by 6.

$$x=\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{7}{3}$$