Solve (x-2)(x+2)/4-3x^2-2x/12+1-2x/3=-1-x/2-frac{5}{4}

$$\frac{ (x-2)(x+2) }{ 4 } - \frac{ 3 { x }^{ 2 } -2x }{ 12 } + \frac{ 1-2x }{ 3 } =- \frac{ 1-x }{ 2 } - \frac{ 5 }{ 4 }$$

Solve for x

$$x = \frac{13}{12} = 1\frac{1}{12} \approx 1.083333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,12,3,2.

$$3\left(x-2\right)\left(x+2\right)-\left(3x^{2}-2x\right)+4\left(1-2x\right)=-6\left(1-x\right)-15$$

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

$$\left(3x-6\right)\left(x+2\right)-\left(3x^{2}-2x\right)+4\left(1-2x\right)=-6\left(1-x\right)-15$$

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

$$3x^{2}-12-\left(3x^{2}-2x\right)+4\left(1-2x\right)=-6\left(1-x\right)-15$$

To find the opposite of 3x^{2}-2x, find the opposite of each term.

$$3x^{2}-12-3x^{2}+2x+4\left(1-2x\right)=-6\left(1-x\right)-15$$

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

$$-12+2x+4\left(1-2x\right)=-6\left(1-x\right)-15$$

Use the distributive property to multiply 4 by 1-2x.

$$-12+2x+4-8x=-6\left(1-x\right)-15$$

Add -12 and 4 to get -8.

$$-8+2x-8x=-6\left(1-x\right)-15$$

Combine 2x and -8x to get -6x.

$$-8-6x=-6\left(1-x\right)-15$$

Use the distributive property to multiply -6 by 1-x.

$$-8-6x=-6+6x-15$$

Subtract 15 from -6 to get -21.

$$-8-6x=-21+6x$$

Subtract 6x from both sides.

$$-8-6x-6x=-21$$

Combine -6x and -6x to get -12x.

$$-8-12x=-21$$

Add 8 to both sides.

$$-12x=-21+8$$

Add -21 and 8 to get -13.

$$-12x=-13$$

Divide both sides by -12.

$$x=\frac{-13}{-12}$$

Fraction \frac{-13}{-12} can be simplified to \frac{13}{12} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{13}{12}$$