Solve 6-(1-2x)+x(4-x)=1-x(2+x)

$$6-(1-2x)+x(4-x)=1-x(2+x)$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

To find the opposite of 1-2x, find the opposite of each term.

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

The opposite of -2x is 2x.

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

Subtract 1 from 6 to get 5.

$$5+2x+x\left(4-x\right)=1-x\left(2+x\right)$$

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

$$5+2x+4x-x^{2}=1-x\left(2+x\right)$$

Combine 2x and 4x to get 6x.

$$5+6x-x^{2}=1-x\left(2+x\right)$$

Use the distributive property to multiply x by 2+x.

$$5+6x-x^{2}=1-\left(2x+x^{2}\right)$$

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

$$5+6x-x^{2}=1-2x-x^{2}$$

Add 2x to both sides.

$$5+6x-x^{2}+2x=1-x^{2}$$

Combine 6x and 2x to get 8x.

$$5+8x-x^{2}=1-x^{2}$$

Add x^{2} to both sides.

$$5+8x-x^{2}+x^{2}=1$$

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

$$5+8x=1$$

Subtract 5 from both sides.

$$8x=1-5$$

Subtract 5 from 1 to get -4.

$$8x=-4$$

Divide both sides by 8.

$$x=\frac{-4}{8}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{2}$$