Solve 2/3left(left(2x-1right)left(x-4right)+3left(x-1/3right)left(1/3+xright)right)=2/3left(5x^2-xright)+frac{14}{9}

$$\frac{ 2 }{ 3 } \left( \left( 2x-1 \right) \left( x-4 \right) +3 \left( x- \frac{ 1 }{ 3 } \right) \left( \frac{ 1 }{ 3 } +x \right) \right) = \frac{ 2 }{ 3 } \left( 5 { x }^{ 2 } -x \right) + \frac{ 14 }{ 9 }$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by x-4 and combine like terms.

$$\frac{2}{3}\left(2x^{2}-9x+4+3\left(x-\frac{1}{3}\right)\left(\frac{1}{3}+x\right)\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Use the distributive property to multiply 3 by x-\frac{1}{3}.

$$\frac{2}{3}\left(2x^{2}-9x+4+\left(3x-1\right)\left(\frac{1}{3}+x\right)\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Use the distributive property to multiply 3x-1 by \frac{1}{3}+x and combine like terms.

$$\frac{2}{3}\left(2x^{2}-9x+4+3x^{2}-\frac{1}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$\frac{2}{3}\left(5x^{2}-9x+4-\frac{1}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Subtract \frac{1}{3} from 4 to get \frac{11}{3}.

$$\frac{2}{3}\left(5x^{2}-9x+\frac{11}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Use the distributive property to multiply \frac{2}{3} by 5x^{2}-9x+\frac{11}{3}.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Use the distributive property to multiply \frac{2}{3} by 5x^{2}-x.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}=\frac{10}{3}x^{2}-\frac{2}{3}x+\frac{14}{9}$$

Subtract \frac{10}{3}x^{2} from both sides.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}-\frac{10}{3}x^{2}=-\frac{2}{3}x+\frac{14}{9}$$

Combine \frac{10}{3}x^{2} and -\frac{10}{3}x^{2} to get 0.

$$-6x+\frac{22}{9}=-\frac{2}{3}x+\frac{14}{9}$$

Add \frac{2}{3}x to both sides.

$$-6x+\frac{22}{9}+\frac{2}{3}x=\frac{14}{9}$$

Combine -6x and \frac{2}{3}x to get -\frac{16}{3}x.

$$-\frac{16}{3}x+\frac{22}{9}=\frac{14}{9}$$

Subtract \frac{22}{9} from both sides.

$$-\frac{16}{3}x=\frac{14}{9}-\frac{22}{9}$$

Subtract \frac{22}{9} from \frac{14}{9} to get -\frac{8}{9}.

$$-\frac{16}{3}x=-\frac{8}{9}$$

Multiply both sides by -\frac{3}{16}, the reciprocal of -\frac{16}{3}.

$$x=-\frac{8}{9}\left(-\frac{3}{16}\right)$$

Multiply -\frac{8}{9} and -\frac{3}{16} to get \frac{1}{6}.

$$x=\frac{1}{6}$$