Solve 2[(x-4)(2x-1)+7]/3-(x-1/4)(1/4+x)=1/3x^2+frac{22}{3}-x+frac{17}{16}

$$\frac { 2 [ ( x - 4 ) ( 2 x - 1 ) + 7 ] } { 3 } - ( x - \frac { 1 } { 4 } ) ( \frac { 1 } { 4 } + x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 22 } { 3 } - x + \frac { 17 } { 16 }$$

Solve for x

$$x=-\frac{1}{5}=-0.2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 48, the least common multiple of 3,4,16.

$$16\times 2\left(\left(x-4\right)\left(2x-1\right)+7\right)-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)=16x^{2}+352-48x+51$$

Multiply 16 and 2 to get 32.

$$32\left(\left(x-4\right)\left(2x-1\right)+7\right)-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)=16x^{2}+352-48x+51$$

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

$$32\left(2x^{2}-9x+4+7\right)-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)=16x^{2}+352-48x+51$$

Add 4 and 7 to get 11.

$$32\left(2x^{2}-9x+11\right)-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)=16x^{2}+352-48x+51$$

Use the distributive property to multiply 32 by 2x^{2}-9x+11.

$$64x^{2}-288x+352-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)=16x^{2}+352-48x+51$$

Add 352 and 51 to get 403.

$$64x^{2}-288x+352-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)=16x^{2}+403-48x$$

Subtract 16x^{2} from both sides.

$$64x^{2}-288x+352-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)-16x^{2}=403-48x$$

Add 48x to both sides.

$$64x^{2}-288x+352-48\left(x-\frac{1}{4}\right)\left(\frac{1}{4}+x\right)-16x^{2}+48x=403$$

Use the distributive property to multiply -48 by x-\frac{1}{4}.

$$64x^{2}-288x+352+\left(-48x+12\right)\left(\frac{1}{4}+x\right)-16x^{2}+48x=403$$

Use the distributive property to multiply -48x+12 by \frac{1}{4}+x and combine like terms.

$$64x^{2}-288x+352-48x^{2}+3-16x^{2}+48x=403$$

Combine 64x^{2} and -48x^{2} to get 16x^{2}.

$$16x^{2}-288x+352+3-16x^{2}+48x=403$$

Add 352 and 3 to get 355.

$$16x^{2}-288x+355-16x^{2}+48x=403$$

Combine 16x^{2} and -16x^{2} to get 0.

$$-288x+355+48x=403$$

Combine -288x and 48x to get -240x.

$$-240x+355=403$$

Subtract 355 from both sides.

$$-240x=403-355$$

Subtract 355 from 403 to get 48.

$$-240x=48$$

Divide both sides by -240.

$$x=\frac{48}{-240}$$

Reduce the fraction \frac{48}{-240} to lowest terms by extracting and canceling out 48.

$$x=-\frac{1}{5}$$