Solve x-x^2+4x+3=x^2-x-(1+2x^2)

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

Solve for x

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

Steps for Solving Linear Equation

Combine x and 4x to get 5x.

$$5x-x^{2}+3=x^{2}-x-\left(1+2x^{2}\right)$$

To find the opposite of 1+2x^{2}, find the opposite of each term.

$$5x-x^{2}+3=x^{2}-x-1-2x^{2}$$

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

$$5x-x^{2}+3=-x^{2}-x-1$$

Add x^{2} to both sides.

$$5x-x^{2}+3+x^{2}=-x-1$$

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

$$5x+3=-x-1$$

Add x to both sides.

$$5x+3+x=-1$$

Combine 5x and x to get 6x.

$$6x+3=-1$$

Subtract 3 from both sides.

$$6x=-1-3$$

Subtract 3 from -1 to get -4.

$$6x=-4$$

Divide both sides by 6.

$$x=\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

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