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

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

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(2x-1\right)\left(2x+1\right)-3\left(x-\frac{1}{3}\right)=6-6\left(2-2x^{2}\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$\left(6x-3\right)\left(2x+1\right)-3\left(x-\frac{1}{3}\right)=6-6\left(2-2x^{2}\right)$$

Use the distributive property to multiply 6x-3 by 2x+1 and combine like terms.

$$12x^{2}-3-3\left(x-\frac{1}{3}\right)=6-6\left(2-2x^{2}\right)$$

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

$$12x^{2}-3-3x+1=6-6\left(2-2x^{2}\right)$$

Add -3 and 1 to get -2.

$$12x^{2}-2-3x=6-6\left(2-2x^{2}\right)$$

Use the distributive property to multiply -6 by 2-2x^{2}.

$$12x^{2}-2-3x=6-12+12x^{2}$$

Subtract 12 from 6 to get -6.

$$12x^{2}-2-3x=-6+12x^{2}$$

Subtract 12x^{2} from both sides.

$$12x^{2}-2-3x-12x^{2}=-6$$

Combine 12x^{2} and -12x^{2} to get 0.

$$-2-3x=-6$$

Add 2 to both sides.

$$-3x=-6+2$$

Add -6 and 2 to get -4.

$$-3x=-4$$

Divide both sides by -3.

$$x=\frac{-4}{-3}$$

Fraction \frac{-4}{-3} can be simplified to \frac{4}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{3}$$