Solve 5(x^2+4)=(x-2)[x+4(x-4)]

$$5 ( x ^ { 2 } + 4 ) = ( x - 2 ) [ x + 4 ( x - 4 ) ]$$

Solve for x

$$x=\frac{6}{13}\approx 0.461538462$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x^{2}+4.

$$5x^{2}+20=\left(x-2\right)\left(x+4\left(x-4\right)\right)$$

Use the distributive property to multiply 4 by x-4.

$$5x^{2}+20=\left(x-2\right)\left(x+4x-16\right)$$

Combine x and 4x to get 5x.

$$5x^{2}+20=\left(x-2\right)\left(5x-16\right)$$

Use the distributive property to multiply x-2 by 5x-16 and combine like terms.

$$5x^{2}+20=5x^{2}-26x+32$$

Subtract 5x^{2} from both sides.

$$5x^{2}+20-5x^{2}=-26x+32$$

Combine 5x^{2} and -5x^{2} to get 0.

$$20=-26x+32$$

Swap sides so that all variable terms are on the left hand side.

$$-26x+32=20$$

Subtract 32 from both sides.

$$-26x=20-32$$

Subtract 32 from 20 to get -12.

$$-26x=-12$$

Divide both sides by -26.

$$x=\frac{-12}{-26}$$

Reduce the fraction \frac{-12}{-26} to lowest terms by extracting and canceling out -2.

$$x=\frac{6}{13}$$