Solve (x-1/3)^2-5x(x+1)=x(2/3-4x)+7/9

$$( x - \frac { 1 } { 3 } ) ^ { 2 } - 5 x ( x + 1 ) = x ( \frac { 2 } { 3 } - 4 x ) + \frac { 7 } { 9 }$$

Solve for x

$$x=-\frac{2}{19}\approx -0.105263158$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{3}\right)^{2}.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}-5x\left(x+1\right)=x\left(\frac{2}{3}-4x\right)+\frac{7}{9}$$

Use the distributive property to multiply x by \frac{2}{3}-4x.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}-5x\left(x+1\right)=\frac{2}{3}x-4x^{2}+\frac{7}{9}$$

Subtract \frac{2}{3}x from both sides.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}-5x\left(x+1\right)-\frac{2}{3}x=-4x^{2}+\frac{7}{9}$$

Add 4x^{2} to both sides.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}-5x\left(x+1\right)-\frac{2}{3}x+4x^{2}=\frac{7}{9}$$

Use the distributive property to multiply -5x by x+1.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}-5x^{2}-5x-\frac{2}{3}x+4x^{2}=\frac{7}{9}$$

Combine x^{2} and -5x^{2} to get -4x^{2}.

$$-4x^{2}-\frac{2}{3}x+\frac{1}{9}-5x-\frac{2}{3}x+4x^{2}=\frac{7}{9}$$

Combine -\frac{2}{3}x and -5x to get -\frac{17}{3}x.

$$-4x^{2}-\frac{17}{3}x+\frac{1}{9}-\frac{2}{3}x+4x^{2}=\frac{7}{9}$$

Combine -\frac{17}{3}x and -\frac{2}{3}x to get -\frac{19}{3}x.

$$-4x^{2}-\frac{19}{3}x+\frac{1}{9}+4x^{2}=\frac{7}{9}$$

Combine -4x^{2} and 4x^{2} to get 0.

$$-\frac{19}{3}x+\frac{1}{9}=\frac{7}{9}$$

Subtract \frac{1}{9} from both sides.

$$-\frac{19}{3}x=\frac{7}{9}-\frac{1}{9}$$

Subtract \frac{1}{9} from \frac{7}{9} to get \frac{2}{3}.

$$-\frac{19}{3}x=\frac{2}{3}$$

Multiply both sides by -\frac{3}{19}, the reciprocal of -\frac{19}{3}.

$$x=\frac{2}{3}\left(-\frac{3}{19}\right)$$

Multiply \frac{2}{3} and -\frac{3}{19} to get -\frac{2}{19}.

$$x=-\frac{2}{19}$$